%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.393", %%% date = "05 August 2024", %%% time = "14:55:12 MDT", %%% filename = "prng.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "43752 119140 515771 5327515", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "AES-NI instruction set; binary Euclidean %%% algorithm for gcd and extended gcd; Common %%% Random Numbers; discrepancy; electrical noise %%% generator; exponential distribution; extended %%% Euclidean algorithm for gcd; generalized %%% feedback shift register (GFSR) generator; %%% Gaussian random number generator; greatest %%% common denominator (GCD); greatest common %%% divisor (GCD); Halton sequences; inversive %%% congruential generator (ICG); lattice point %%% distribution; lava lamp; linear congruential %%% generator (LCG); linear feedback shift %%% register (LFSR) generator; logarithmic %%% distribution; Mersenne Twister; modular %%% inverse; Monte Carlo; multiplicative %%% congruential generator (MCG); %%% multiply-with-carry (MWC) generator; %%% nonuniform distribution; normal distribution; %%% normal number; Philox generator; Poisson %%% distribution; pseudorandom number generator %%% (PRNG); quantum noise generator; quasi-Monte %%% Carlo; random-number generator (RNG); random %%% variables; random variates; RANDU; RdRand %%% instruction; rn01; true random number %%% generator; uniform distribution; ziggurat %%% method", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This file collects references on pseudorandom %%% number generation, sampling, selection, %%% simulation, distribution, and testing. Such %%% numbers are used in many different fields %%% (reflected in their descriptions in articles %%% in more than 570 different journals). While %%% entries in this bibliography are drawn from a %%% large corpus of bibliographic data (more than %%% 1,593,000 entries in Summer 2020), coverage is %%% necessarily selective. Nevertheless, most of %%% the important publications in the field that %%% are frequently referenced by others are %%% likely to be found here. Particular %%% attention is given to including historical %%% sources. %%% %%% The related, and huge, field of Monte Carlo %%% techniques is touched only by fewer than 160 %%% entries. The introduction in entry %%% James:1980:MCT provides two reasonable %%% definitions: %%% %%% * ``A Monte Carlo technique is any technique %%% making use of random numbers to solve a %%% problem.'' %%% %%% * ``the Monte Carlo method is defined as %%% representing the solution of a problem as a %%% parameter of a hypothetical population, and %%% using a random sequence of numbers to %%% construct a sample of the population, from %%% which statistical estimates of the %%% parameter can be obtained.'' %%% %%% At version 1.393, the year coverage looked %%% like this: %%% %%% 1900 ( 1) 1942 ( 5) 1984 ( 50) %%% 1901 ( 0) 1943 ( 5) 1985 ( 60) %%% 1902 ( 0) 1944 ( 5) 1986 ( 64) %%% 1903 ( 0) 1945 ( 1) 1987 ( 61) %%% 1904 ( 0) 1946 ( 2) 1988 ( 87) %%% 1905 ( 0) 1947 ( 3) 1989 ( 88) %%% 1906 ( 0) 1948 ( 8) 1990 ( 123) %%% 1907 ( 0) 1949 ( 10) 1991 ( 85) %%% 1908 ( 1) 1950 ( 8) 1992 ( 121) %%% 1909 ( 1) 1951 ( 15) 1993 ( 107) %%% 1910 ( 0) 1952 ( 6) 1994 ( 130) %%% 1911 ( 0) 1953 ( 15) 1995 ( 121) %%% 1912 ( 0) 1954 ( 19) 1996 ( 108) %%% 1913 ( 0) 1955 ( 9) 1997 ( 91) %%% 1914 ( 1) 1956 ( 21) 1998 ( 106) %%% 1915 ( 0) 1957 ( 9) 1999 ( 81) %%% 1916 ( 1) 1958 ( 16) 2000 ( 80) %%% 1917 ( 0) 1959 ( 19) 2001 ( 105) %%% 1918 ( 0) 1960 ( 24) 2002 ( 91) %%% 1919 ( 0) 1961 ( 34) 2003 ( 74) %%% 1920 ( 0) 1962 ( 26) 2004 ( 78) %%% 1921 ( 0) 1963 ( 24) 2005 ( 79) %%% 1922 ( 2) 1964 ( 33) 2006 ( 83) %%% 1923 ( 0) 1965 ( 27) 2007 ( 69) %%% 1924 ( 0) 1966 ( 23) 2008 ( 133) %%% 1925 ( 1) 1967 ( 33) 2009 ( 118) %%% 1926 ( 0) 1968 ( 36) 2010 ( 130) %%% 1927 ( 2) 1969 ( 32) 2011 ( 121) %%% 1928 ( 0) 1970 ( 46) 2012 ( 85) %%% 1929 ( 1) 1971 ( 36) 2013 ( 53) %%% 1930 ( 1) 1972 ( 55) 2014 ( 43) %%% 1931 ( 2) 1973 ( 39) 2015 ( 40) %%% 1932 ( 0) 1974 ( 46) 2016 ( 35) %%% 1933 ( 3) 1975 ( 38) 2017 ( 36) %%% 1934 ( 3) 1976 ( 63) 2018 ( 33) %%% 1935 ( 0) 1977 ( 39) 2019 ( 31) %%% 1936 ( 1) 1978 ( 42) 2020 ( 15) %%% 1937 ( 2) 1979 ( 51) 2021 ( 18) %%% 1938 ( 6) 1980 ( 47) 2022 ( 22) %%% 1939 ( 7) 1981 ( 33) 2023 ( 16) %%% 1940 ( 1) 1982 ( 35) 2024 ( 10) %%% 1941 ( 4) 1983 ( 50) %%% 19xx ( 1) %%% 20xx ( 3) %%% %%% Article: 2873 %%% Book: 232 %%% InBook: 4 %%% InCollection: 82 %%% InProceedings: 512 %%% Manual: 11 %%% MastersThesis: 16 %%% Misc: 95 %%% PhdThesis: 20 %%% Proceedings: 159 %%% TechReport: 208 %%% Unpublished: 2 %%% %%% Total entries: 4214 %%% %%% Users of random-number generators need to be %%% aware that much of what has been published in %%% the field before about 1990 has largely been %%% obsoleted by newer methods, because the %%% generated sequences of random numbers have %%% been shown to be defective in one or more %%% ways. Examples of such deficiencies include: %%% %%% * lack of randomness, or correlations, in %%% sequences of bits within single numbers; %%% %%% * correlations between number subsequences; %%% %%% * correlations at constant stepsizes in the %%% number sequences (see the famous paper %%% Marsaglia:1968:RNF); %%% %%% * short periods that are too readily %%% exhausted (in 2010, periods of $2^{32}$ can %%% be traversed in a few seconds, and periods %%% of $2^{64}$ can be covered in about 30 %%% minutes on one million cores: see entry %%% Salmon:2011:PRN); %%% %%% * fragility with respect to user-specific %%% initial seeds, with some seeds producing %%% good sequences, and other seeds, bad %%% sequences, usually without warning; %%% %%% * fragility with respect to internal generator %%% algorithm parameters (for example, with the %%% long-used linear congruential generators, %%% just one satisfactory 32-bit multiplier was %%% found for every 1,300,000 multipliers %%% tested; see entries Fishman:1986:EAM and %%% Park:1988:RNG); %%% %%% * fragility with respect to nonunit steps in %%% the sequences (for a linear congruential %%% generator, sampling every n-th value can be %%% shown to be equivalent to a different %%% choice of multiplier and constant, and that %%% choice may exhibit strong correlations, %%% even if the original parameters have been %%% shown to produce largely-satisfactory %%% sequences: see entry Marsaglia:1968:RNF, %%% and page 12 of entry Coddington:1997:RNG); %%% %%% * impracticality for parallel computation %%% because of the need for excessive internal %%% state (see entry Salmon:2011:PRN); %%% %%% * inability to produce independent %%% simultaneous streams of random numbers from %%% the generator, as is needed in parallel %%% computations; %%% %%% * lack of algorithm details; %%% %%% * lack of cross-platform portability, such as %%% through dependence on low-level %%% architecture-dependent (and even %%% chip-model-dependent) details of computer %%% arithmetic; %%% %%% * lack of source-code access; %%% %%% * lack of knowledge of generator period, %%% generator interval, and generator interval %%% end points; %%% %%% * difficulty of implementing in common %%% programming languages; %%% %%% * need for multiple-precision arithmetic, %%% or excessive computation for a single %%% random number; %%% %%% * large Monte Carlo computations in physics %%% and chemistry have sometimes been shown to %%% be extremely sensitive to long-range %%% corrections in sequences of random numbers, %%% and may even converge to an incorrect %%% answer with one generator, and a correct %%% result with another (see entries %%% Coldwell:1974:CDS, Kalle:1984:PRN, %%% Berdnicov:1991:MCS, Ferrenberg:1992:MCS, %%% Grassberger:1993:CGR, Kankaala:1993:BLC, %%% Selke:1993:CFM, Coddington:1994:ARN, %%% Holian:1994:PNG, Vattulainen:1994:PTR, %%% Compagner:1995:OCR, Schmid:1995:EMC, %%% Vattulainen:1995:CSS, Vattulainen:1995:PMT, %%% Bromley:1996:QNG, Coddington:1997:RNG, %%% Shchur:1997:CMC, Shchur:1997:SDR, %%% DSouza:1998:SBD, Gammel:1998:HRR, %%% Resende:1998:URN, Mertens:2003:EPR, %%% Bauke:2004:PRC, Mertens:2004:EPR, %%% Ossola:2004:SED, Hongo:2010:RNG, %%% Click:2011:QRN, and Ghersi:2017:CQR). %%% %%% An ideal pseudorandom-number generator must %%% be able to produce identical sequences on all %%% platforms on which it can be made to run. %%% Otherwise, it is impossible to reproduce a %%% numerical experiment, violating one of the %%% key tenets of the scientific method. It is %%% also impossible to debug a program that %%% cannot be made to run reproducibly. In %%% addition, an identical stream of random %%% numbers is essential if one is to compare %%% multiple statistical models of some process; %%% otherwise, it is likely to be difficult to %%% assign differences in predictions of the %%% models as due to features of those models, or %%% just due to variations in input data. Papers %%% in the modeling, simulation, and statistics %%% literature refer to such streams with the %%% capitalized phrase Common Random Numbers %%% (CRN) and describe them as `variance %%% reducing' (see chapter 11 of entries %%% Law:1991:SMA, Law:2000:SMA, and Law:2006:SMA, %%% and, in year order, entries %%% Kleijnen:1975:AVC, Heikes:1976:UCR, %%% Heidelberger:1979:CSS, Kleijnen:1979:ASC, %%% Wright:1979:ECR, Gal:1984:OEC, %%% Clark:1986:BSP, Kleijnen:1988:ASE, %%% Yang:1989:OUC, Yang:1991:UCR, %%% Glasserman:1992:SGG, Kleijnen:1992:RMS, %%% Nelson:1992:CRN, Nelson:1993:CVM, %%% Nelson:1993:RMC, Nelson:1995:UCR, %%% Dai:1997:RCD, Kleinman:1999:SBO, and %%% Chick:2001:NPS). See also this article: %%% %%% http://en.wikipedia.org/wiki/Variance_reduction %%% %%% While there are many algorithms for uniformly %%% distributed pseudorandom numbers that have %%% the essential property of reproducible %%% streams, most methods for converting such %%% numbers to nonuniform distributions cannot %%% make that guarantee. Repairing such defects %%% remains an open research problem. %%% %%% For lengthy treatments of the problem of %%% converting random numbers from uniform %%% distributions to nonuniform ones, see, in %%% year order, Knuth:1976:CNR, Devroye:1986:NUR, %%% Law:1991:SMA (chapter 8), Hormann:1993:QNU, %%% Schrift:1993:UTN, Cheng:1998:RVG, %%% Law:2000:SMA (chapter 8), Leydold:2002:FPN, %%% Hormann:2004:ANR, Beliakov:2005:UNR, %%% Law:2006:SMA (chapter 8), Cowles:2007:BRA, %%% deSchryver:2010:NHE, and LEcuyer:2011:NUR, %%% %%% Several publications listed here cover the %%% early, and pre-, history of the use of random %%% numbers in sampling and simulation. Besides %%% the several bibliographies cited later, see %%% particularly these entries (in year order): %%% Pearson:1900:CGS, Student:1908:PEM, %%% Ore:1948:NTH, Brown:1949:HRR, Brown:1951:HRR, %%% Hull:1962:RNG, Teichroew:1965:HDS, and %%% Good:1969:HRR. %%% %%% Before computers became available, generating %%% random numbers was a tedious and error-prone %%% task, and several compilations of such %%% numbers, and comments on them, were published %%% to reduce the burden on others. Various %%% believed-to-be random sources, including %%% electromechanical devices, roulette wheels, %%% shuffled cards, and drawing from large %%% collections of numbered objects, were used to %%% generate the tabulated random numbers. For %%% the years prior to 1960, see entries (in year %%% order) Tippett:1927:RSN, %%% Mahalanobis:1934:TRS, Kermack:1937:SDA, %%% Kermack:1937:TRS, Fisher:1938:STB, %%% Kendall:1938:RRS,o Nair:1938:TRS, %%% Yule:1938:TTR, Kendall:1939:SPR, %%% Peatman:1942:TRN, Fisher:1943:STB, %%% Gage:1943:CTR, Swed:1943:TTR, Brown:1948:STR, %%% Wold:1948:RND, Brown:1949:HRR, %%% Fisher:1949:STB, Stevens:1949:TRD, %%% Brown:1951:HRR, Forsythe:1951:GTRa, %%% Forsythe:1951:GTRb, Tippett:1952:RSN, %%% Fisher:1953:STBa, Fisher:1953:STBb, %%% Meyer:1954:GTR, Schwartz:1954:RPC, %%% Fieller:1955:CRN, RAND:1955:MRD, %%% Tompkins:1956:RJS, Tompkins:1956:RMR, %%% Fisher:1957:STBa, Fisher:1957:STBb, %%% Sengupta:1958:TRN, Sterzer:1959:RNG, %%% Thomson:1959:EMS, and Tippett:1959:RSN. %%% %%% Entry Yule:1927:RS documents the problems of %%% bias introduced when humans, even %%% well-intentioned and disinterested ones, %%% record data. %%% %%% I. J. Good remarks in entry Good:1969:HRR %%% ``Various tables of random digits have been %%% published. As the editor, Ernest Rubin, says, %%% these are all random, but some are more %%% random than others. The question has been %%% asked `Can a table of random digits have just %%% one misprint?' This will be left as an %%% exercise for the reader.'' %%% %%% Several entries in this bibliography are for %%% publications that describe physical devices %%% for generating random numbers from haphazard %%% phenomena, such as acoustic, electrical, or %%% optical noise, lava lamps, quantum %%% interference, and radioactive decay. While %%% such numbers are likely to be humanly %%% ``unpredictable'', they are not necessarily %%% ``uniformly random'' in the sense that large %%% collections of random numbers on [0,1] should %%% be uniformly distributed over the unit %%% interval, and have a limiting average of 1/2: %%% tests of some of those devices have shown %%% biases in favor of lower or higher values. %%% %%% Entries Kubota:1995:DRE, Mikov:1996:LSA, %%% Gentle:1990:CIR, and Saiprasert:2010:OHA %%% discuss rounding errors when random numbers %%% from one range are converted to numbers in %%% another range. %%% %%% See entries Gentle:1990:CIR, %%% Mascagni:2000:ASS, and Brent:2006:FRR for %%% good discussions of desirable properties for %%% algorithms and software for generation of %%% random numbers. %%% %%% The question of when a sequence of digits, in %%% some specified base, is random was apparently %%% first raised in 1909 (see entry %%% Borel:1909:PDL, and the remark in entry %%% Borel:1914:LTF). Such numbers are called %%% ``normal numbers'', but only a few have been %%% proved to have that property, the first %%% perhaps being Champernowne's number (see %%% entry Champernowne:1933:CDN). The constant %%% pi is believed to be a normal number, but the %%% proof remains elusive; see Chapter 4 of entry %%% Borwein:2004:MEP. Normality does NOT mean %%% that short digit sequences are random: the %%% sequences 0123456789 and 7777777777 both %%% occur within the first 22,900,000,000 decimal %%% digits of pi. The six-digit sequence 999999 %%% appears at the 762nd decimal place, and is %%% called the ``Feynman point'', after Physics %%% Nobel laureate Richard Feynman: for %%% background, see %%% %%% http://en.wikipedia.org/wiki/Feynman_point %%% %%% Most algorithmic random-number generators %%% produce a sequence of distinct integers that %%% eventually repeats, and the count of values %%% produced to that point is called the %%% ``period''. Adjacent numbers are never %%% identical, unlike the digits of a normal %%% number. %%% %%% For testing the quality of random-number %%% generators, most of the early recommendations %%% (e.g., see extensive coverage in %%% Knuth:1997:SA) have the problem that while %%% they may readily identify really bad %%% generators, they are rarely helpful in %%% distinguishing the mediocre from the good, %%% and good from the superb. What is instead %%% needed is a suite of several sophisticated %%% tests, and experience with those tests on a %%% variety of generators. Notable examples of %%% such test facilities include the Marsaglia %%% Diehard Test Suite (entries %%% Marsaglia:1985:CVR and Marsaglia:1996:DBT), %%% the L'Ecuyer/Simard TestU01 suite (entries %%% LEcuyer:2001:TSL, LEcuyer:2002:TSL, %%% LEcuyer:2006:TSL, and LEcuyer:2007:TCL), the %%% Marsaglia/Tsang tuftest suite (entry %%% Marsaglia:2002:SDP), and the NIST 800-22 %%% suite (entry Rukhin:2001:STS). See also %%% entry Haramoto:2009:AST for a discussion of %%% how adaptive testing can be used to %%% distinguish test failure (indicated by %%% p-values close to 0 or 1) from algorithm %%% failure. %%% %%% Such test facilities need to be available at %%% all end-user sites where random-number %%% generator code is compiled, used, or written, %%% so that researchers can verify for themselves %%% whether the generator that they are using has %%% the expected properties of randomness. %%% Subtle differences in compiler %%% code-generation order, compiler errors, and %%% model-dependent hardware variations, can all %%% be sources of outright generator failure, or %%% worse (because the failure might not be %%% detected), substandard quality. In %%% particular, it is essential to record in %%% program output the initial seeds, as well as %%% short selected sequences of random numbers, %%% such as the first and last 100 numbers %%% generated in a run. Also, no single %%% simulation should be trusted until it has %%% been compared with results obtained from one %%% or more completely-different generators. %%% %%% Researchers and software designers who %%% contemplate using, or producing, random %%% number generators for serious, and %%% widespread, use need to be aware of the %%% impact of their algorithm choice on the %%% reliability of results of models based on %%% random numbers. For a story of how an entire %%% field of research was put at risk by a poor %%% choice in a widely-used software package, see %%% entry Umlauft:2009:GNS. %%% %%% In this bibliographer's view, relatively few %%% of the many journals in which random-number %%% algorithms have been proposed have been found %%% to be generally-reliable sources in this %%% area. Examples of recommended journals %%% include the ones abbreviated j-CACM, %%% j-IBM-JRD, j-IBM-SYS-J, j-JACM, %%% j-J-COMPUT-APPL-MATH, j-PARALLEL-COMPUTING, %%% j-TOMACS, and j-TOMS, all of whose %%% random-number articles should be present in %%% this bibliography. %%% %%% While there are many authors of the %%% publications listed in this bibliography, a %%% few stand out by having made large numbers of %%% important, influential, and insightful %%% contributions. They include George %%% Marsaglia, Pierre L'Ecuyer, Juergen %%% Eichenauer-Herrmann, Harald Niederreiter, and %%% Richard P. Brent. Their deep understanding, %%% and clear writing, on the problems of %%% generating and testing pseudorandom numbers %%% is worthy of study. See also Marsaglia's %%% publication bibliography at %%% %%% https://www.math.utah.edu/pub/bibnet/authors/m/ %%% %%% At version 0.56, this file was extended with %%% the 148 bibliography entries given in a fine %%% survey \cite{Hull:1962:RNG}; its authors %%% report on their first page: %%% %%% ``The bibliography is intended to be %%% complete with respect to references %%% concerned with the generation of random %%% numbers on computers. It contains %%% substantially all such references to the %%% open literature, as well as many %%% references to government and company %%% reports. In addition it contains a number %%% of references concerning each of the %%% related topics which are considered in %%% this paper.'' %%% %%% The numbered entries from that bibliography %%% are identified by HDnumber values in entries %%% in this file. %%% %%% While it is impossible to claim completeness %%% in a subject-specific bibliography, their %%% work nevertheless gives a good survey of what %%% was known about computer generation of %%% pseudo-random numbers in early 1962. Since %%% then, the literature on the subject has %%% exploded, and covers far more material than %%% we can usefully collect here. In particular, %%% the unavoidable correlations in congruential %%% generators were not known until six years %%% later (Marsaglia:1968:RNF), and the %%% cryptographic insecurities of many generators %%% were not even considered by Hull and Dobell %%% in 1962 (see Shi:1975:SRP, Reeds:1977:CRN, %%% Reeds:1979:CMC, Plumstead:1982:ISG, %%% Plumstead:1983:ISP, Blum:1984:HGC, %%% Frieze:1984:LCG, Knuth:1985:DLC, %%% Stern:1987:SLC, Frieze:1988:RTI, %%% Lagarias:1988:UEP, Shi:1988:SRP %%% Boyar:1989:ISPa, Boyar:1989:ISPb, %%% Krawczyk:1990:HPC, Brickell:1992:CSR, %%% Krawczyk:1992:HPC, Schneier:1996:ACP, %%% Bach:1998:EPM, Marsaglia:2003:RNG, %%% Contini:2005:SAA, Gutierrez:2007:ISP, %%% Rose:2011:KBT, and Gutierrez:2013:PML). %%% %%% The annotated bibliographies of Sowey %%% (Sowey:1972:CCB, Sowey:1978:SCB, %%% Sowey:1986:TCB) contain 300 references from %%% 1927 to 1971 (6.7/year), 130 references from %%% 1972 to 1976 (26/year), and 300 references %%% from 1977--1984 (37/year), demonstrating the %%% publication growth. Entry Page:1967:GPR %%% also contains a bibliography of earlier work, %%% and entry Sahai:1980:SSB supplements Sowey's %%% work. Another early bibliography is entry %%% Nance:1972:BRN. %%% %%% A search of the IEEE eXplore database for the %%% decade 2000--2009 found 522 articles with %%% titles containing 'pseudo-random', %%% `pseudorandom', and `pseudo random', or about %%% 52/year. The MathSciNet database shows about %%% 31/year for that period. %%% %%% A Google Scholar search for the same period %%% finds 1130 article titles with %%% `pseudorandom', 1400 with `pseudo-random', %%% 1480 with `pseudo random', and 846 with %%% `random number generator', or about 485/year. %%% %%% Warning: Cryptographic applications of random %%% numbers may have quite different requirements %%% than modeling, sampling, and simulation do, %%% and sequence reproducibility is likely to be %%% undesirable, because the random numbers are %%% used to generate secret, and unguessable, %%% cryptographic keys. It is possible that even %%% a limited sequence of random values from an %%% algorithmic generator can be used to reveal %%% properties and parameters of that generator, %%% and thus allow prediction of past and future %%% values. Such a crack has already been %%% demonstrated for linear congruential %%% generators: see the remarks above on %%% cryptographic insecurities of random-number %%% streams. Attacks on other algorithms have %%% also been demonstrated: see entries %%% Kannan:1988:PFN and Just:1990:IRA. Instead, %%% hardware-assisted sources of truly random %%% numbers may be needed. Examples include the %%% Intel AES-NI instruction-set extension (see %%% entry Salmon:2011:PRN), the Intel RdRand %%% instruction (see entry Taylor:2011:DR), the %%% pseudodevices /dev/random and /dev/urandom on %%% various Unix flavors, and cryptographic %%% accelerator boards available from some %%% hardware vendors. Just because the random %%% numbers come from a physical device does NOT %%% mean that they are necessarily uniformly %%% distributed, or pass tests of randomness: %%% see, for example, entry Tsoi:2003:CFB. %%% %%% Entries in this bibliography that discuss %%% generation of random numbers from physical %%% sources have the phrase ``true random numbers %%% from physical sources'' in their keywords %%% values. See also %%% %%% http://en.wikipedia.org/wiki/Comparison_of_hardware_random_number_generators %%% http://en.wikipedia.org/wiki/Hardware_random_number_generator %%% http://en.wikipedia.org/wiki//dev/random %%% %%% See entries Gutmann:2004:CSA, Barak:2005:MAP, %%% and Gutterman:2006:ALR for discussion of the %%% problem of generating data for hardware %%% pseudodevices, the problem of code complexity %%% and excessive patching, and demonstration of %%% bugs and other flaws that affect %%% cryptographic uses and compromise system %%% security, despite the large effort in %%% designing, and then widely deploying, such %%% devices. The last-cited paper notes: ``[the %%% Linux pseudodevice] complexity does not %%% improve its security but rather hides its %%% weaknesses. We suggest that future %%% constructions of pseudo-random number %%% generators follow the BH (Barak--Halevi) %%% construction (and in general, try to `keep it %%% simple').'' %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" # "\ifx \cftil \undefined \def \cftil#1{\~#1} \fi" # "\ifx \undefined \cprime \def \cprime {$'$} \fi" # "\ifx \undefined \flqq \def \flqq {\ifmmode \ll \else \leavevmode \raise 0.2ex \hbox{$\scriptscriptstyle \ll $}\fi}\fi" # "\ifx \undefined \frqq \def \frqq {\ifmmode \gg \else \leavevmode \raise 0.2ex \hbox{$\scriptscriptstyle \gg $}\fi}\fi" # "\ifx \undefined \k \let \k = \c \fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" # "\ifx \undefined \mathbf \def \mathbf #1{{\bf #1}}\fi" # "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}}\fi" # "\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi" # "\ifx \undefined \scr \let \scr = \cal \fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} @String{ack-r-project= "R Project Team"}

%%% ==================================================================== %%% Institution abbreviations:

@String{inst-ARGONNE= "Argonne National Laboratory"} @String{inst-ARGONNE:adr= "Argonne, IL, USA"} @String{inst-ATT-BELL= "AT\&T Bell Laboratories"} @String{inst-ATT-BELL:adr= "Murray Hill, NJ, USA"} @String{inst-BOEING-SRL= "Boeing Scientific Research Laboratories"} @String{inst-BOEING-SRL:adr= "Seattle, WA, USA"} @String{inst-LANL= "Los Alamos National Laboratory"} @String{inst-LANL:adr= "Los Alamos, NM, USA"} @String{inst-LASL= "Los Alamos Scientific Laboratory"} @String{inst-LASL:adr= "Los Alamos, NM, USA"} @String{inst-MATHWORKS= "The MathWorks, Inc."} @String{inst-MATHWORKS:adr= "3 Apple Hill Drive, Natick, MA 01760-2098, USA"} @String{inst-SRC-IDA= "Supercomputing Research Center: IDA"} @String{inst-SRC-IDA:adr= "Lanham, MD, USA"} @String{inst-STAN-CS= "Stanford University, Department of Computer Science"} @String{inst-STAN-CS:adr= "Stanford, CA, USA"} @String{inst-UIUC-CSRD= "University of Illinois at Urbana-Champaign, Center for Supercomputing Research and Development"} @String{inst-UIUC-CSRD:adr= "Urbana, IL 61801, USA"} @String{inst-UTAH-MATH= "University of Utah, Department of Mathematics"} @String{inst-UTAH-MATH:adr= "Salt Lake City, UT 84112-0090, USA"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ABH-MATH-SEMIN-UNIV-HAMBG= "Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg"} @String{j-ABSTR-PAP-AM-CHEM-SOC= "Abstracts of Papers of the {American Chemical Society}"} @String{j-ACM-COMM-COMP-ALGEBRA= "ACM Communications in Computer Algebra"} @String{j-ACTA-ARITHMETICA= "Acta Arithmetica"} @String{j-ACTA-CRYSTAL-A-FOUND-CRYST= "Acta crystallographica. Section A, Foundations of crystallography"} @String{j-ACTA-MATH-HUNG= "Acta mathematica Academiae Scientiarum Hungaricae"} @String{j-ACTA-MATH-SINICA= "Acta Mathematica Sinica (New Series)"} @String{j-ADA-LETT= "Ada Letters"} @String{j-ADA-USER-J= "Ada User Journal"} @String{j-ADV-APPL-MATH= "Advances in Applied Mathematics"} @String{j-ADV-APPL-PROB= "Advances in Applied Probability"} @String{j-ADV-APPL-STAT= "Advances and Applications in Statistics"} @String{j-ADV-COMPUT-MATH= "Advances in Computational Mathematics"} @String{j-ADV-MATH= "Advances in Mathematics"} @String{j-ADV-SCI-LETT= "Advanced Science Letters"} @String{j-AIP-CONF-PROC= "AIP Conference Proceedings"} @String{j-ALGORITHMICA= "Algorithmica"} @String{j-ALGORITHMS-BASEL= "Algorithms ({Basel})"} @String{j-AM-J-MATH-MANAGE-SCI= "American Journal of Mathematical and Management Sciences"} @String{j-AM-SCI= "American Scientist"} @String{j-AMER-J-PHYSICS= "American Journal of Physics"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-AMER-STAT= "The American Statistician"} @String{j-ANG-INFO-ELEK-DATEN= "Angewandte Informatik (Elektron. Datenverarbeitung)"} @String{j-ANN-APPL-PROBAB= "Annals of Applied Probability"} @String{j-ANN-HIST-COMPUT= "Annals of the History of Computing"} @String{j-ANN-INST-STAT-MATH-TOKYO= "Annals of the Institute of Statistical Mathematics (Tokyo)"} @String{j-ANN-MAT-PURA-APPL-4= "Annali di matematica pura ed applicata. Series 4"} @String{j-ANN-MATH= "Annals of Mathematics"} @String{j-ANN-MATH-STAT= "Annals of Mathematical Statistics"} @String{j-ANN-NY-ACAD-SCI= "Annals of the New York Academy of Sciences"} @String{j-ANN-OPER-RESEARCH= "Annals of Operations Research"} @String{j-ANN-PROBAB= "Annals of Probability"} @String{j-ANN-STAT= "Annals of Statistics"} @String{j-ANZIAM-J= "The ANZIAM Journal"} @String{j-ANZJS= "Australian \& New Zealand Journal of Statistics"} @String{j-APPL-ALGEBRA-ENG-COMMUN-COMPUT= "Applicable algebra in engineering, communication and computing"} @String{j-APPL-MATH-COMP= "Applied Mathematics and Computation"} @String{j-APPL-MATH-LETT= "Applied Mathematics Letters"} @String{j-APPL-MATH-SER-NBS= "Applied Mathematics Series / National Bureau of Standards"} @String{j-APPL-NUM-MATH= "Applied Numerical Mathematics: Transactions of IMACS"} @String{j-APPL-OPTICS= "Applied Optics"} @String{j-APPL-PHYS-EXPRESS= "Applied Physics Express"} @String{j-APPL-PHYS-LET= "Applied Physics Letters"} @String{j-APPL-STAT= "Applied Statistics"} @String{j-ARCH-MATH= "Archiv der Mathematik"} @String{j-ARS-COMB= "Ars Combinatoria. The Canadian Journal of Combinatorics"} @String{j-ATT-BELL-LAB-TECH-J= "AT\&T Bell Laboratories Technical Journal"} @String{j-ATT-TECH-J= "AT\&T Technical Journal"} @String{j-AUST-J-STAT= "Australian Journal of Statistics"} @String{j-AUSTRALIAN-COMP-J= "Australian Computer Journal"} @String{j-AUSTRALIAN-J-PHYS= "Australian Journal of Physics"} @String{j-AUTOMATION-REMOTE-CTL= "Automation and Remote Control"} @String{j-BEHAV-RES-METH-INSTR= "Behavior Research Methods and Instrumentation"} @String{j-BEHAV-RES-METH-INSTR-COMP= "Behavior Research Methods, Instruments, and Computers"} @String{j-BELL-SYST-TECH-J= "The Bell System Technical Journal"} @String{j-BIOMETRICAL-J= "Biometrical Journal"} @String{j-BIOMETRIKA= "Biometrika"} @String{j-BIT= "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH= "BIT Numerical Mathematics"} @String{j-BOLL-UNIONE-MAT-ITAL= "Bollettino della Unione matematica italiana"} @String{j-BULL-AMS= "Bulletin of the American Mathematical Society"} @String{j-BULL-INST-MATH-STAT= "Bulletin --- Institute of Mathematical Statistics"} @String{j-BYTE= "BYTE Magazine"} @String{j-C-PLUS-PLUS-REPORT= "C++ Report"} @String{j-C-R-ACAD-SCI-PARIS-SER-AB= "Comptes Rendus Hebdomadaires des S{\'e}ances de l'Acad{\'e}mie des Sciences. S{\'e}ries A et B"} @String{j-CACM= "Communications of the ACM"} @String{j-CAD= "Computer Aided Design"} @String{j-CALCOLO= "Calcolo: a quarterly on numerical analysis and theory of computation"} @String{j-CAN-J-MATH= "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques"} @String{j-CAN-MATH-BULL= "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques"} @String{j-CCCUJ= "C/C++ Users Journal"} @String{j-CCPE= "Concurrency and Computation: Prac\-tice and Experience"} @String{j-CGF= "Computer Graphics Forum"} @String{j-CGIP= "Computer Graphics and Image Processing"} @String{j-CHANCE= "Chance"} @String{j-CHAOS-SOLITONS-FRACTALS= "Chaos, Solitons \& Fractals"} @String{j-CHIFFRES= "Chiffres: Revue de l'Association fran{\c{c}}aise de Calcul"} @String{j-CHIN-PHYS-LETT= "Chinese Physics Letters"} @String{j-COLLEGE-MATH-J= "College Mathematics Journal"} @String{j-COLLOQ-MATH-BOLYAI= "Colloquia Mathematica Societatis J{\'a}nos Bolyai"} @String{j-COMBIN-PROBAB-COMPUT= "Combinatorics, Probability and Computing"} @String{j-COMBINATORICA= "Combinatorica"} @String{j-COMM-NONLIN-SCI-NUM-SIM= "Communications in Nonlinear Science and Numerical Simulation"} @String{j-COMM-STAT= "Communications in Statistics"} @String{j-COMMUN-STAT-THEORY-METH= "Communications in Statistics: Theory and Methods"} @String{j-COMMUN-INF-SYST= "Communications in Information and Systems"} @String{j-COMMUN-STAT-SIMUL-COMPUT= "Communications in Statistics: Simulation and Computation"} @String{j-COMP-AUTO= "Computers and Automation"} @String{j-COMP-GEOSCI= "Computers and Geosciences"} @String{j-COMP-J= "The Computer Journal"} @String{j-COMP-LANG-MAG= "Computer Language Magazine"} @String{j-COMP-LANGS= "Computer Languages"} @String{j-COMP-MATH= "Computational Mathematics"} @String{j-COMP-NET-AMSTERDAM= "Computer Networks (Amsterdam, Netherlands: 1999)"} @String{j-COMP-REV= "Computing Reviews"} @String{j-COMP-STAT= "Computational Statistics"} @String{j-COMP-SURV= "ACM Computing Surveys"} @String{j-COMPUT-MATH-APPL= "Computers and Mathematics and Applications"} @String{j-COMPUT-MATH-APPL-B= "Computers and Mathematics with Applications. Part B"} @String{j-COMPUT-SOFTW-BIG-SCI= "Computing and Software for Big Science"} @String{j-COMP-OP-RES= "Computers and Operations Research"} @String{j-COMP-PHYS-COMM= "Computer Physics Communications"} @String{j-COMPUT-PHYS= "Computers in Physics"} @String{j-COMPUT-SECUR= "Computers \& Security"} @String{j-COMPUT-AND-BIOMED-RES= "Computers and Biomedical Research"} @String{j-COMPUT-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-COMPUT-BULL= "The Computer Bulletin"} @String{j-COMPUT-IND-ENG= "Computers \& Industrial Engineering"} @String{j-COMPUT-METH-PROG-BIOMED= "Computer Methods and Programs in Biomedicine"} @String{j-COMPUT-PROGRAMS-BIOMED= "Computer Programs in Biomedicine"} @String{j-COMPUT-SCI-ENG= "Computing in Science and Engineering"} @String{j-COMPUT-STAT-DATA-ANAL= "Computational Statistics \& Data Analysis"} @String{j-COMPUT-STAT-Q= "Computational Statistics Quarterly"} @String{j-COMPUT-SYST-SCI-ENG= "Computer Systems Science and Engineering"} @String{j-COMPUTABILITY= "Computability"} @String{j-COMPUTER= "Computer"} @String{j-COMPUTERS-AND-GRAPHICS= "Computers and Graphics"} @String{j-COMPUTING= "Computing: Archiv f{\"u}r Informatik und Numerik"} @String{j-CONTEMP-MATH= "Contemporary Mathematics (American Mathematical Society)"} @String{j-CRYPTOGR-COMMUN= "Cryptography and Communications"} @String{j-CRYPTOLOGIA= "Cryptologia"} @String{j-CUJ= "C Users Journal"} @String{j-CVGIP= "Computer Vision, Graphics, and Image Processing"} @String{j-CVGIP-GMIP= "Computer Vision, Graphics, and Image Processing. Graphical Models and Image Processing"} @String{j-CVGIP-IU= "Computer Vision, Graphics, and Image Processing. Image Understanding"} @String{j-CYBER= "Cybernetics"} @String{j-CZECH-J-PHYS= "Czechoslovak Journal of Physics"} @String{j-CZECH-MATH-J= "Czechoslovak mathematical journal = Chekhoslovatskii matematicheskii zhurnal"} @String{j-DDJ= "Dr. Dobb's Journal of Software Tools"} @String{j-DESIGNS-CODES-CRYPTOGR= "Designs, Codes, and Cryptography"} @String{j-DISTRIB-COMPUT= "Distributed Computing"} @String{j-DOKL-AKAD-NAUK= "Doklady Akademii Nauk SSSR"} @String{j-DUKE-MATH-J= "Duke Mathematical Journal"} @String{j-ECONOMETRICA= "Econometrica"} @String{j-EDU-PSYCH-MEASUREMENT= "Educational and Psychological Measurement"} @String{j-ELECT-LETTERS= "Electronics Letters"} @String{j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI= "Electronics and communications in Japan. Part 3, Fundamental electronic science"} @String{j-ELECTRON-COMMUN-PROBAB= "Electronic Communications in Probability"} @String{j-ELECTRON-ENG= "Electronic Engineering"} @String{j-ELECTRON-J-PROBAB= "Electronic Journal of Probability"} @String{j-ELECTRON-TRANS-NUMER-ANAL= "Electronic Transactions on Numerical Analysis (ETNA)"} @String{j-ELECTRONIC-DESIGN= "Electronic Design"} @String{j-ELECTRONICS= "Electronics"} @String{j-ELEK-INFO-KYBER= "Elektronische Informationsverarbeitung und Kybernetik (EIK)"} @String{j-ESAIM-PROBAB-STATIST= "ESAIM: Probability and Statistics"} @String{j-EUR-J-OPER-RES= "European Journal of Operational Research"} @String{j-EUR-J-PHYS= "European Journal of Physics"} @String{j-EUR-PHYS-J-SPEC-TOP= "European Physical Journal --- Special Topics"} @String{j-EURASIP-J-EMBED-SYS= "EURASIP Journal on Embedded Systems"} @String{j-EUROPHYS-LETT= "Europhysics Letters"} @String{j-EXP-MATH= "Experimental Mathematics"} @String{j-FIB-QUART= "Fibonacci Quarterly"} @String{j-FINITE-FIELDS-APPL= "Finite Fields and their Applications"} @String{j-FORTRAN-FORUM= "ACM Fortran Forum"} @String{j-FUT-GEN-COMP-SYS= "Future Generation Computer Systems"} @String{j-FUTURE-INTERNET= "Future Internet"} @String{j-GEOBYTE= "Geobyte"} @String{j-HEWLETT-PACKARD-J= "Hew\-lett-Pack\-ard Journal: technical information from the laboratories of Hew\-lett-Pack\-ard Company"} @String{j-IBM-JRD= "IBM Journal of Research and Development"} @String{j-IBM-SYS-J= "IBM Systems Journal"} @String{j-IBM-TDB= "IBM Technical Disclosure Bulletin"} @String{j-IEE-PROC-COMPUT-DIGIT-TECH= "IEE Proceedings. Computers and Digital Techniques"} @String{j-IEE-PROC-E= "IEE proceedings, E: Computers and digital techniques"} @String{j-IEEE-ANN-HIST-COMPUT= "IEEE Annals of the History of Computing"} @String{j-IEEE-CGA= "IEEE Computer Graphics and Applications"} @String{j-IEEE-COMMUN-LET= "IEEE Communications Letters"} @String{j-IEEE-COMPUT-ARCHIT-LETT= "IEEE Computer Architecture Letters"} @String{j-IEEE-COMPUT-SCI-ENG= "IEEE Computational Science \& Engineering"} @String{j-IEEE-DES-TEST-COMPUT= "IEEE Design \& Test of Computers"} @String{j-IEEE-INT-SYMP-INF-THEORY= "IEEE International Symposium on Information Theory"} @String{j-IEEE-J-SOLID-STATE-CIRCUITS= "IEEE Journal of Solid-State Circuits"} @String{j-IEEE-MICRO= "IEEE Micro"} @String{j-IEEE-PHOTONICS-TECHNOL-LETT= "IEEE Photonics Technology Letters"} @String{j-IEEE-SEC-PRIV= "IEEE Security \& Privacy"} @String{j-IEEE-SPECTRUM= "IEEE Spectrum"} @String{j-IEEE-TRANS-APPL-SUPERCOND= "IEEE Transactions on Applied Superconductivity"} @String{j-IEEE-TRANS-BIG-DATA= "IEEE Transactions on Big Data"} @String{j-IEEE-TRANS-CAD-ICS= "IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"} @String{j-IEEE-TRANS-CIRCUITS-SYST= "IEEE Transactions on Circuits and Systems"} @String{j-IEEE-TRANS-CIRCUITS-SYST-1= "IEEE Transactions on Circuits and Systems I: Regular Papers"} @String{j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL= "IEEE Transactions on Circuits and Systems I: Fundamental Theory and Application"} @String{j-IEEE-TRANS-COMM= "IEEE Transactions on Communications"} @String{j-IEEE-TRANS-COMPUT= "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-ELEC-COMPUT= "IEEE Transactions on Electronic Computers"} @String{j-IEEE-TRANS-EMERG-TOP-COMPUT= "IEEE Transactions on Emerging Topics in Computing"} @String{j-IEEE-TRANS-INF-FOREN-SEC= "IEEE Transactions on Information Forensics and Security"} @String{j-IEEE-TRANS-INF-THEORY= "IEEE Transactions on Information Theory"} @String{j-IEEE-TRANS-INSTRUM-MEAS= "IEEE Transactions on Instrumentation and Measurement"} @String{j-IEEE-TRANS-NETWORKING= "IEEE\slash ACM Transactions on Networking"} @String{j-IEEE-TRANS-NUCL-SCI= "IEEE Transactions on Nuclear Science"} @String{j-IEEE-TRANS-PAR-DIST-SYS= "IEEE Transactions on Parallel and Distributed Systems"} @String{j-IEEE-TRANS-POWER-DELIV= "IEEE Transactions on Power Delivery"} @String{j-IEEE-TRANS-RELIAB= "IEEE Transactions on Reliability"} @String{j-IEEE-TRANS-SOFTW-ENG= "IEEE Transactions on Software Engineering"} @String{j-IEEE-TRANS-VLSI-SYST= "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"} @String{j-IIE-TRANS= "IIE Transactions"} @String{j-IJCSS= "International Journal of Computer Science and Security (IJCSS)"} @String{j-IJSAHPC= "The International Journal of Supercomputer Applications and High Performance Computing"} @String{j-ILL-J-MATH= "Illinois Journal of Mathematics"} @String{j-IMAGE-VIS-COMPUT= "Image and Vision Computing"} @String{j-INDAG-MATH= "Indagationes Mathematic{\ae}"} @String{j-INF-CONTROL= "Information and Control"} @String{j-INFO-PROC-LETT= "Information Processing Letters"} @String{j-INFOR= "INFOR"} @String{j-INFORMS-J-COMPUT= "INFORMS Journal on Computing"} @String{j-INSUR-MATH-ECON= "Insurance, Mathematics and Economics"} @String{j-INT-J-APPL-CRYPTOGR= "International Journal of Applied Cryptography. IJACT"} @String{j-INT-J-APPROX-REASONING= "International Journal of Approximate Reasoning"} @String{j-INT-J-CIRCUIT-THEORY-APPL= "International Journal of Circuit Theory and Applications"} @String{j-INT-J-COMPUT-APPL= "International Journal of Computer Applications"} @String{j-INT-J-COMPUT-MATH= "International Journal of Computer Mathematics"} @String{j-INT-J-COMPUT-INF-SCI= "International Journal of Computer and Information Sciences"} @String{j-INT-J-FOUND-COMP-SCI= "International Journal of Foundations of Computer Science (IJFCS)"} @String{j-INT-J-HIGH-SPEED-COMPUTING= "International Journal of High Speed Computing (IJHSC)"} @String{j-INT-J-INFO-SEC= "International Journal of Information Security"} @String{j-INT-J-MATH-EDU-SCI-TECH= "International Journal of Mathematical Education in Science and Technology"} @String{j-INT-J-MATH-MATH-SCI= "International Journal of Mathematics and Mathematical Sciences"} @String{j-INT-J-MOD-PHYS-C= "International Journal of Modern Physics C [Physics and Computers]"} @String{j-INT-J-MODELLING-SIMUL= "International Journal of Modelling and Simulation"} @String{j-INT-J-NUMBER-THEORY= "International Journal of Number Theory"} @String{j-INT-J-PARALLEL-PROG= "International Journal of Parallel Programming"} @String{j-INT-J-PAR-EMER-DIST-SYS= "International Journal of Parallel, Emergent and Distributed Systems: IJPEDS"} @String{j-INT-J-THEOR-PHYS= "International Journal of Theoretical Physics"} @String{j-INT-STAT-REV= "International Statistical Review = Revue Internationale de Statistique"} @String{j-INT-STUD-PHILOS-SCI= "International Studies in the Philosophy of Science"} @String{j-INTERFACE= "Interface"} @String{j-INTERFACES= "Interfaces"} @String{j-IRE-TRANS-ELEC-COMPUT= "IRE Transactions on Electronic Computers"} @String{j-J-ACM= "Journal of the ACM"} @String{j-J-ACOUST-SOC-AM= "Journal of the Acoustical Society of America"} @String{j-J-ALG= "Journal of Algorithms"} @String{j-J-AM-STAT-ASSOC= "Journal of the American Statistical Association"} @String{j-J-APPL-ECONOMETRICS= "Journal of Applied Econometrics"} @String{j-J-APPL-PHYS= "Journal of Applied Physics"} @String{j-J-APPL-PROBAB= "Journal of Applied Probability"} @String{j-J-APPL-STAT= "Journal of Applied Statistics"} @String{j-J-ASTRONAUTICAL-SCIENCES= "Journal of the Astronautical Sciences"} @String{j-J-CHEM-PHYS= "Journal of Chemical Physics"} @String{j-J-CHEM-THEORY-COMPUT= "Journal of Chemical Theory and Computation"} @String{j-J-COMP-SECUR= "Journal of Computer Security"} @String{j-J-COMP-SYS-SCI= "Journal of Computer and System Sciences"} @String{j-J-COMPLEXITY= "Journal of Complexity"} @String{j-J-COMPUT-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-CHEM= "Journal of Computational Chemistry"} @String{j-J-COMPUT-GRAPH-STAT= "Journal of Computational and Graphical Statistics"} @String{j-J-COMPUT-PHYS= "Journal of Computational Physics"} @String{j-J-COMPUT-SCI= "Journal of Computational Science"} @String{j-J-CRYPTO-ENG= "Journal of Cryptographic Engineering"} @String{j-J-CRYPTOLOGY= "Journal of Cryptology: the journal of the International Association for Cryptologic Research"} @String{j-J-DISCR-MATH-SCI-CRYPTO= "Journal of Discrete Mathematical Sciences and Cryptography"} @String{j-J-ECON-DYN-CONTROL= "Journal of Economic Dynamics and Control"} @String{j-J-ECON-LIT= "Journal of Economic Literature"} @String{j-J-FUNCT-PROGRAM= "Journal of Functional Programming"} @String{j-J-INF-OPTIM-SCI= "Journal of Information \& Optimization Sciences"} @String{j-J-INFO-SEC-APPL= "Journal of Information Security and Applications (JISA)"} @String{j-J-JAPAN-SOC-COMPUT-STAT= "Journal of Japanese Society of Computational Statistics"} @String{j-J-LOND-MATH-SOC= "Journal of the London Mathematical Society"} @String{j-J-MATH-ARTS= "Journal of Mathematics and the Arts"} @String{j-J-MATH-CRYPTOL= "Journal of Mathematical Cryptology"} @String{j-J-MATH-KYOTO-UNIV= "Journal of Mathematics of Kyoto University"} @String{j-J-MATH-PHYS= "Journal of Mathematical Physics"} @String{j-J-MOD-APPL-STAT-METH= "Journal of Modern Applied Statistical Methods"} @String{j-J-MOD-OPT= "Journal of Modern Optics"} @String{j-J-NETW-COMPUT-APPL= "Journal of Network and Computer Applications"} @String{j-J-NUMBER-THEORY= "Journal of Number Theory"} @String{j-J-NUMER-METHODS-COMPUT-APPL= "Journal on Numerical Methods and Computer Applications"} @String{j-J-OPER-RES-SOC= "OR: the journal of the Operational Research Society"} @String{j-J-OPER-RES-SOC-JPN= "Journal of the Operations Research Society of Japan"} @String{j-J-PAR-DIST-COMP= "Journal of Parallel and Distributed Computing"} @String{j-J-PARAPSYCHOL= "Journal of Parapsychology"} @String{j-J-PAS-ADA-MOD= "Journal of Pascal, Ada and Modula-2"} @String{j-J-PHILOS-LOGIC= "Journal of Philosophical Logic"} @String{j-J-PHYS-A= "Journal of Physics A (Mathematical and General)"} @String{j-J-PHYS-CHEM-B= "Journal of Physical Chemistry. B. Condensed matter, materials, surfaces, interfaces \& biophysical"} @String{j-J-PHYS-E= "Journal of Physics. E: Scientific Instruments"} @String{j-J-PSYCHOL= "Journal of Psychology"} @String{j-J-R-STAT-SOC= "Journal of the Royal Statistical Society"} @String{j-J-R-STAT-SOC-SER-A-GENERAL= "Journal of the Royal Statistical Society. Series A (General)"} @String{j-J-R-STAT-SOC-SER-B-METHODOL= "Journal of the Royal Statistical Society. Series B (Methodological)"} @String{j-J-R-STAT-SOC-SER-D-STATISTICIAN= "Journal of the Royal Statistical Society. Series D (The Statistician)"} @String{j-J-RES-NATL-BUR-STAND-1934= "Journal of Research of the National Bureau of Standards (1934)"} @String{j-J-RES-NATL-BUR-STAND-B= "Journal of Research of the National Bureau of Standards. Section B, Mathematics and Mathematical Physics"} @String{j-J-SIAM= "Journal of the Society for Industrial and Applied Mathematics"} @String{j-J-SIMUL= "Journal of Simulation"} @String{j-J-STAT-COMPUT-SIMUL= "Journal of Statistical Computation and Simulation"} @String{j-J-STAT-PHYS= "Journal of Statistical Physics"} @String{j-J-STAT-PLANN-INFERENCE= "Journal of Statistical Planning and Inference"} @String{j-J-STAT-SOFT= "Journal of Statistical Software"} @String{j-J-STAT-THEORY-PRACT= "Journal of Statistical Theory and Practice"} @String{j-J-SUPERCOMPUTING= "The Journal of Supercomputing"} @String{j-J-SYMBOLIC-COMP= "Journal of Symbolic Computation"} @String{j-J-SYST-SOFTW= "The Journal of Systems and Software"} @String{j-J-UCS= "J.UCS: Journal of Universal Computer Science"} @String{j-J-VLSI-SIGNAL-PROC= "Journal of VLSI Signal Processing"} @String{j-J-WASH-ACAD-SCI= "Journal of the Washington Academy of Sciences"} @String{j-JAPAN-J-INDUST-APPL-MATH= "Japan Journal of Industrial and Applied Mathematics"} @String{j-JETC= "ACM Journal on Emerging Technologies in Computing Systems (JETC)"} @String{j-JETP-LETT= "JETP Letters"} @String{j-LASER-PHYS-LETT= "Laser Physics Letters"} @String{j-LECT-NOTES-COMP-SCI= "Lecture Notes in Computer Science"} @String{j-LECT-NOTES-CONTROL-INF-SCI= "Lecture Notes in Control and Information Sciences"} @String{j-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} @String{j-LIGHTWAVE-TECHNOL= "Journal of Lightwave Technology"} @String{j-LINEAR-ALGEBRA-APPL= "Linear Algebra and its Applications"} @String{j-LOGIN= ";login: the USENIX Association newsletter"} @String{j-LOS-ALAMOS-SCIENCE= "Los Alamos Science"} @String{j-MANAGEMENT-SCIENCE= "Management Science"} @String{j-MANUSCR-MATH= "Manuscripta Mathematica"} @String{j-MAPLE-TECH-NEWS= "Maple Technical Newsletter"} @String{j-MATH-ANN= "Mathematische Annalen"} @String{j-MATH-COMP-MODELLING= "Mathematical and Computer Modelling"} @String{j-MATH-COMP-SIM= "Mathematics and Computers in Simulation"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-MATH-GEOL= "Mathematical Geology"} @String{j-MATH-INTEL= "The Mathematical Intelligencer"} @String{j-MATH-JAPON= "Mathematica Japonica"} @String{j-MATH-OP-RES= "Mathematics of Operations Research"} @String{j-MATH-PROG= "Mathematical Programming"} @String{j-MATH-PROG-STUDY= "Mathematical Programming Study"} @String{j-MATH-REV= "Mathematical Reviews"} @String{j-MATH-SCAND= "Mathematica Scandinavica"} @String{j-MATH-SCI-ENG= "Mathematics in Science and Engineering"} @String{j-MATH-SLOVACA= "Mathematica Slovaca"} @String{j-MATH-TABLES-OTHER-AIDS-COMPUT= "Mathematical Tables and Other Aids to Computation"} @String{j-MATH-Z= "Mathematische Zeitschrift"} @String{j-MATHEMATICA-J= "Mathematica Journal"} @String{j-MDMV= "Mitteilungen der Deutschen Mathematiker-Vereinigung"} @String{j-MEASUREMENT= "Measurement: Journal of the International Measurement Confederation"} @String{j-METRIKA= "Metrika. 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%%% ==================================================================== %%% Publishers and their addresses:

@String{pub-A-K-PETERS= "A. K. Peters, Ltd."} @String{pub-A-K-PETERS:adr= "Wellesley, MA, USA"} @String{pub-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, NY, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AEGEAN-PARK= "Aegean Park Press"} @String{pub-AEGEAN-PARK:adr= "Laguna Hills, CA, USA"} @String{pub-AFIPS= "AFIPS Press"} @String{pub-AFIPS:adr= "Montvale, NJ, USA"} @String{pub-AIP= "American Institute of Physics"} @String{pub-AIP:adr= "Woodbury, NY, USA"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-ARTECH= "Artech House Inc."} @String{pub-ARTECH:adr= "Norwood, MA, USA"} @String{pub-ASME= "American Society of Mechanical Engineers"} @String{pub-ASME:adr= "345 E. 47th St., New York, NY 10017, USA"} @String{pub-AW= "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr= "Reading, MA, USA"} @String{pub-BIRKHAUSER-BOSTON= "Birkh{\"a}user Boston Inc."} @String{pub-BIRKHAUSER-BOSTON:adr= "Cambridge, MA, USA"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-CHAPMAN-HALL= "Chapman and Hall, Ltd."} @String{pub-CHAPMAN-HALL:adr= "London, UK"} @String{pub-CHAPMAN-HALL-CRC= "Chapman and Hall/CRC"} @String{pub-CHAPMAN-HALL-CRC:adr= "Boca Raton, FL, USA"} @String{pub-CLARENDON= "Clarendon Press"} @String{pub-CLARENDON:adr= "New York, NY, USA"} @String{pub-CRC= "CRC Press"} @String{pub-CRC:adr= "2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-CSLI= "CSLI Publications"} @String{pub-CSLI:adr= "Stanford, CA, USA"} @String{pub-DEKKER= "Marcel Dekker, Inc."} @String{pub-DEKKER:adr= "New York, NY, USA"} @String{pub-DOVER= "Dover Publications, Inc."} @String{pub-DOVER:adr= "New York, NY, USA"} @String{pub-ELLIS-HORWOOD= "Ellis Horwood"} @String{pub-ELLIS-HORWOOD:adr= "New York, NY, USA"} @String{pub-ELS= "Elsevier Science Publishers B.V."} @String{pub-ELS:adr= "Amsterdam, The Netherlands"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-ELSEVIER-ACADEMIC= "Elsevier Academic Press"} @String{pub-ELSEVIER-ACADEMIC:adr= "Amsterdam, The Netherlands"} @String{pub-FREE= "Free Press"} @String{pub-FREE:adr= "New York, NY, USA"} @String{pub-GAUTHIER-VILLARS= "Gauthier-Villars"} @String{pub-GAUTHIER-VILLARS:adr= "Paris, France"} @String{pub-HARVARD= "Harvard University Press"} @String{pub-HARVARD:adr= "Cambridge, MA, USA"} @String{pub-HMSO= "Her Majesty's Stationary Office"} @String{pub-HMSO:adr= "London, England"} @String{pub-HOLDEN-DAY= "Holden-Day"} @String{pub-HOLDEN-DAY:adr= "San Francisco, CA, USA"} @String{pub-IBM= "IBM Corporation"} @String{pub-IBM:adr= "Poughkeepsie, NY, USA"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-MCGRAW-HILL= "Mc{\-}Graw-Hill"} @String{pub-MCGRAW-HILL:adr= "New York, NY, USA"} @String{pub-MIT= "MIT Press"} @String{pub-MIT:adr= "Cambridge, MA, USA"} @String{pub-MORGAN-KAUFMANN= "Morgan Kaufmann Publishers"} @String{pub-MORGAN-KAUFMANN:adrsf= "San Francisco, CA, USA"} @String{pub-NAP= "National Academy Press"} @String{pub-NAP:adr= "Washington, DC, USA"} @String{pub-NBS= "U.S. National Bureau of Standards"} @String{pub-NBS:adr= "Gaithersburg, MD, USA"} @String{pub-NIST= "National Institute for Standards and Technology"} @String{pub-NIST:adr= "Gaithersburg, MD, USA"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OLIVER-BOYD= "Oliver and Boyd"} @String{pub-OLIVER-BOYD:adr= "Edinburgh, UK; London, UK"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PALGRAVE-MACMILLAN= "Palgrave Macmillan"} @String{pub-PALGRAVE-MACMILLAN:adr= "Houndmills, Basingstoke, Hampshire England and New York, NY, USA"} @String{pub-PANTHEON= "Pantheon Books"} @String{pub-PANTHEON:adr= "New York, NY, USA"} @String{pub-PERGAMON= "Pergamon"} @String{pub-PERGAMON:adr= "New York, NY, USA"} @String{pub-PETROCELLI-CHARTER= "Petrocelli\slash Charter"} @String{pub-PETROCELLI-CHARTER:adr= "New York, NY, USA"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Upper Saddle River, NJ, USA"} @String{pub-PHYSICA-VERLAG= "Physica-Verlag"} @String{pub-PHYSICA-VERLAG:adr= "Vienna, Austria"} @String{pub-PLENUM= "Plenum Press"} @String{pub-PLENUM:adr= "New York, NY, USA; London, UK"} @String{pub-PRINCETON= "Princeton University Press"} @String{pub-PRINCETON:adr= "Princeton, NJ, USA"} @String{pub-R-E-KRIEGER= "Robert E. Krieger Publishing Company"} @String{pub-R-E-KRIEGER:adr= "Huntington, NY, USA"} @String{pub-REIDEL= "D. Reidel"} @String{pub-REIDEL:adr= "Dordrecht, The Netherlands; Boston, MA, USA; Lancaster, UK; Tokyo, Japan"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SOC-COMPUT-SIM= "Society for Computer Simulation"} @String{pub-SOC-COMPUT-SIM:adr= "San Diego, CA, USA"} @String{pub-SPIE= "Society of Photo-optical Instrumentation Engineers (SPIE)"} @String{pub-SPIE:adr= "Bellingham, WA, USA"} @String{pub-STANFORD= "Stanford University Press"} @String{pub-STANFORD:adr= "Stanford, CA, USA"} @String{pub-SUN-MICROSYSTEMS-PRESS= "Sun Microsystems Press"} @String{pub-SUN-MICROSYSTEMS-PRESS:adr= "Palo Alto, CA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-TAYLOR-FRANCIS= "Taylor and Francis"} @String{pub-TAYLOR-FRANCIS:adr= "Boca Raton, FL, USA"} @String{pub-TEUBNER= "Teubner"} @String{pub-TEUBNER:adr= "Stuttgart, Germany; Leipzig, Germany"} @String{pub-U-CAL= "University of California Press"} @String{pub-U-CAL:adr= "Berkeley, CA, USA"} @String{pub-U-MICHIGAN= "University of Michigan Press"} @String{pub-U-MICHIGAN:adr= "Ann Arbor, MI, USA"} @String{pub-U-NC= "University of North Carolina Press"} @String{pub-U-NC:adr= "Chapel Hill, NC, USA"} @String{pub-NORTON= "W. W. Norton \& Co."} @String{pub-NORTON:adr= "New York, NY, USA"} @String{pub-USENIX= "USENIX"} @String{pub-USENIX:adr= "Berkeley, CA, USA"} @String{pub-USGPO= "United States Government Printing Office"} @String{pub-USGPO:adr= "Washington, DC, USA"} @String{pub-VAN-NOSTRAND-REINHOLD= "Van Nostrand Reinhold"} @String{pub-VAN-NOSTRAND-REINHOLD:adr= "New York, NY, USA"} @String{pub-W-H-FREEMAN= "W. H. {Freeman and Company}"} @String{pub-W-H-FREEMAN:adr= "New York, NY, USA"} @String{pub-WI= "Wiley-In{\-}ter{\-}sci{\-}ence"} @String{pub-WI:adr= "New York, NY, USA"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr= "P. O. Box 128, Farrer Road, Singapore 9128"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-APPL-MATH-SER-NBS= "Applied Mathematics Series / National Bureau of Standards"} @String{ser-BOSTON-STUD-PHILOS-SCI= "Boston Studies in the Philosophy of Science"} @String{ser-LECT-NOTES-MATH= "Lecture Notes in Mathematics"} @String{ser-LNCS= "Lecture Notes in Computer Science"} @String{ser-LNMATH= "Lecture Notes in Mathematics"}

%%% ==================================================================== %%% Bibliography entries, sorted by year, and then by citation label:

@Article{Pearson:1900:CGS, author = "Karl Pearson", title = "On a Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such That it can be Reasonably Supposed to Have Arisen in Random Sampling", journal = j-PHIL-MAGAZINE, volume = "50", number = "302", pages = "157--175", month = jul # "\slash " # dec, year = "1900", CODEN = "PHMAA4", DOI = "https://doi.org/10.1080/14786440009463897", ISSN = "0031-8086", bibdate = "Thu Jan 05 10:58:18 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.tandfonline.com/doi/pdf/10.1080/14786440009463897", acknowledgement = ack-nhfb, fjournal = "The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science", journal-URL = "http://www.tandfonline.com/loi/tphm19", remark = "This is the paper in which Pearson introduces the chi-square measure, which the magazine Science 84 (November 1984) ranked among the top twenty scientific discoveries of the 20th Century that changed our lives.", } @Article{Student:1908:PEM, author = "{Student}", title = "The Probable Error of a Mean", journal = j-BIOMETRIKA, volume = "6", number = "1", pages = "1--25", month = mar, year = "1908", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2331554", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 13:37:25 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315351; https://www.math.utah.edu/pub/tex/bib/biometrika1900.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2331554", acknowledgement = ack-nhfb, fjournal = "Biometrika", HDnumber = "116", journal-URL = "http://www.jstor.org/journals/00063444.html", remark = "Was the author really W. S. Gossett?", } @Article{Borel:1909:PDL, author = "{\'E}mile Borel", title = "Les probabilit{\'e}s d{\'e}nombrables et leurs applications arithm{\'e}tiques. ({French}) [{Countable} probabilities and their arithmetic applications]", journal = j-REND-CIRC-MAT, volume = "27", number = "??", pages = "247--271", month = "????", year = "1909", CODEN = "RCMMAR", DOI = "https://doi.org/10.1007/BF03019651", ISSN = "0009-725X (print), 1973-4409 (electronic)", ISSN-L = "0009-725X", bibdate = "Thu Dec 22 08:18:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://springerlink.com/content/121284", ZMnumber = "40.0283.01", acknowledgement = ack-nhfb, fjournal = "Rendiconti del Circolo Matematico di Palermo (1884--1940)", language = "French", remark = "This is believed to be the paper in which Borel introduced the notion of a ``normal number'', one whose digits, in a specified base, are truly random. On page 260, Borel writes: ``La probabilit{\'e} {\em pour que la fr{\'e}quence totale d'un chiffre d{\'e}termin{\'e} existe et soit {\'e}gale {\`a} $ 1 / 10 $ \/} a pour valeur l'unit{\'e}. La probabilit{\'e} pour que la fr{\'e}quence des dix chiffres existe et soit {\'e}gale {\`a} $ 1 / 10 $ pour chacun d'eux a aussi pour valeur l'unit{\'e}. Lorsque la condition pr{\'e}c{\'e}dente est r{\'e}alis{\'e} par une fraction d{\'e}cimale, nous dirons que le nombre {\'e}gal {\`a} cette fraction est {\em simplement normal\/} par rapport {\`a} la base $ 10 $. Un nombre simplement normal est done caract{\'e}ris{\'e} par le fait que, $ c_0, c_1, c_2, \ldots {}, c_8, c_9 $ d{\'e}signant les nombres respectifs de fois que figurent les chiffres $ 0, 1, 2, \ldots {}, 8, 9 $ parmi les $n$ premi{\`e}res d{\'e}cimales, chacun des rapports: $ c_0 / n, c_1 / n, c_1 / n, \ldots {}, c_8 / n, c_9 / n $ a pour limite $ 1 / 10 $ lorsque $n$ augmente ind{\`e}finiment.'' [The probability that the total frequency determined by a number exists and is equal to $ 1 / 10 $ is set to unity. The likelihood that the frequency of the ten digits exists and is equal to $ 1 / 10 $ for each value is also unity. When the condition above is satisfied by a decimal fraction, we say that the number equal to this fraction is simply normal to the base $ 10 $. A simply-normal number is thus characterized by the fact that, $ c_0, c_1, c_2, \ldots {}, c_8, c_9 $ representing the respective number of times that the digits $ 0, 1, 2, \ldots {}, 8, 9 $ among the first $n$ decimals, each of the ratios $ c_0 / n, c_1 / n, c_1 / n, \ldots {}, c_8 / n, c_9 / n $ has the limit $ 1 / 10 $ when $n$ increases without limit.]", remark-2 = "Submitted from Paris on 3 November 1908.", } @Book{Borel:1914:LTF, author = "{\'E}mile Borel", title = "Le{\c{c}}ons sur la Th{\'e}orie des Fonctions. ({French}) [{Lectures} on the theory of functions]", publisher = pub-GAUTHIER-VILLARS, address = pub-GAUTHIER-VILLARS:adr, edition = "Second", pages = "x + 259", year = "1914", LCCN = "????", bibdate = "Wed Dec 21 06:24:41 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, author-dates = "1871--1956", language = "French", remark = "First edition 1898. On pages 182--216, this book introduced the notion of a normal number: roughly, one whose digits are random. From \cite[page 242]{Kannan:1988:PFN}: ``When are the bits of a real number random? (The phrase 'the bits of a real number' will mean the binary expansion of the fractional part of the number.) The classical definition was provided by Borel in 1909 \cite{Borel:1909:PDL,Borel:1914:LTF}. The gist of it follows: Define a real number $a$ to be normal with respect to the base $2$ if for any natural number $k$, each of the $ 2^k $ possible $0$--$1$ strings of length $k$ occur with equal probability in the bits of $a$. A similar definition can be made for other bases. It was not difficult to show that most real numbers are normal. It was shown by Champernowne \cite{Champernowne:1933:CDN} in 1933 that the real number $ a_0 $ which equals the infinite decimal $ .123456789101112 \ldots {} $ (whose digits are obtained by juxtaposing the digits of the integers $ 1, 2, 3, 4, \ldots {} $ ) is normal to the base $ 10 $. Copeland and Erdos generalized this to any basis and a class of reals including $ a_0 $ and $ a_1 = 0.2357111317 \ldots {} $ whose digits are obtained by juxtaposing the digits of successive primes.''", } @Article{Weyl:1916:GZM, author = "H. Weyl", title = "{{\"U}ber die Gleichverteilung Zahlen modulo Eins}. ({German}) [{On} the uniform distribution of numbers modulo one]", journal = j-MATH-ANN, volume = "77", number = "3", pages = "313--352", month = sep, year = "1916", CODEN = "MAANA3", DOI = "https://doi.org/10.1007/BF01475864", ISSN = "0025-5831 (print), 1432-1807 (electronic)", ISSN-L = "0025-5831", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://resolver.sub.uni-goettingen.de/purl?GDZPPN002266423", acknowledgement = ack-nhfb, fjournal = "Mathematische Annalen", HDnumber = "140", journal-URL = "http://link.springer.com/journal/208", language = "German", } @Article{Fisher:1922:ICT, author = "R. A. Fisher", title = "On the Interpretation of $ \chi^2 $ from Contingency Tables, and the Calculation of {$P$}", journal = j-J-R-STAT-SOC, volume = "85", number = "1", pages = "87--94", month = jan, year = "1922", CODEN = "????", ISSN = "0952-8385", bibdate = "Mon Jan 16 14:58:16 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2340521", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society", journal-URL = "http://www.jstor.org/journals/09528385.html", } @Article{Yule:1922:AMA, author = "G. Udny Yule", title = "On the application of the $ \chi^2 $ method to association and contingency tables, with experimental illustrations", journal = j-J-R-STAT-SOC, volume = "85", number = "1", pages = "95--104", month = jan, year = "1922", CODEN = "????", ISSN = "0952-8385", bibdate = "Mon Jan 16 14:58:16 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2340522", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society", journal-URL = "http://www.jstor.org/journals/09528385.html", } @Article{Tippett:1925:EIR, author = "L. H. C. Tippett", title = "On the Extreme Individuals and the Range of Samples Taken from a Normal Population", journal = j-BIOMETRIKA, volume = "17", number = "3/4", pages = "364--387", month = dec, year = "1925", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2332087", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 13:38:03 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315377; https://www.math.utah.edu/pub/tex/bib/biometrika1920.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2332087", acknowledgement = ack-nhfb, fjournal = "Biometrika", HDnumber = "122", journal-URL = "http://www.jstor.org/journals/00063444.html", } @Book{Tippett:1927:RSN, author = "Leonard Henry Caleb Tippett", title = "Random sampling numbers", volume = "15", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "viii + 26", year = "1927", LCCN = "QA47 .T7 no. 15", bibdate = "Mon Jun 27 13:35:14 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "With a foreword by editor Karl Pearson.", series = "Tracts for computers", acknowledgement = ack-nhfb, HDnumber = "123", remark = "At head of title: Department of applied statistics (Computing section) University of London, University college. At the time, the term `computer' in the series title referred to a human calculational drudge, using female.", subject = "Mathematics; Tables; Sampling (Statistics)", } @Article{Yule:1927:RS, author = "G. Udny Yule", title = "On Reading a Scale", journal = j-J-R-STAT-SOC, volume = "90", number = "3", pages = "570--587", month = "????", year = "1927", CODEN = "????", ISSN = "0952-8385", bibdate = "Wed Nov 23 12:29:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See related later work \cite{Preece:1981:DFD}.", URL = "http://www.jstor.org/stable/2341205", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society", journal-URL = "http://www.jstor.org/journals/09528385.html", remark = "This paper reports on human bias in the recording of last digits in measurements, or from roundings, or from later scale conversions.", } @Article{Klein:1929:SSD, author = "O. Klein and T. Nishina", title = "{{\"U}ber die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac}. ({German}) [{On} the scattering of radiation by free electrons according to the new relativistic quantum dynamics of {Dirac}]", journal = j-Z-PHYSIK, volume = "52", number = "11--12", pages = "853--868", month = nov, year = "1929", CODEN = "ZEPYAA", DOI = "https://doi.org/10.1007/BF01366453", ISSN = "0044-3328", bibdate = "Mon Feb 27 10:09:18 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "This paper introduces the Klein--Nishina distribution of random numbes.", URL = "http://www.springerlink.com/content/p6606272608242k2/", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Physik}", journal-URL = "http://link.springer.com/journal/218", language = "German", } @Article{Baker:1930:RSN, author = "G. A. Baker", title = "Random sampling from non-homogeneous populations", journal = j-METRON, volume = "8", number = "??", pages = "67--88", month = "????", year = "1930", CODEN = "MRONAM", ISSN = "0026-1424 (print), 2281-695X (electronic)", ISSN-L = "0026-1424", bibdate = "Mon Jan 16 14:20:14 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/metron1930.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Metron", } @Article{Ward:1931:DRS, author = "Morgan Ward", title = "The distribution of residues in a sequence satisfying a linear recursion relation", journal = j-TRANS-AM-MATH-SOC, volume = "33", number = "1", pages = "166--190", month = "????", year = "1931", CODEN = "TAMTAM", DOI = "https://doi.org/10.2307/1989465", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "11A07 (39A10)", MRnumber = "1501583", bibdate = "Wed Nov 12 08:28:33 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Trans. AMS", fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", remark = "Cited in \cite[page 34]{Reiser:1977:AAR}", } @Article{Wilson:1931:DCS, author = "Edwin B. Wilson and Margaret M. Hilferty", title = "The distribution of chi-square", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "17", number = "12", pages = "684--688", day = "1", month = dec, year = "1931", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.17.12.684", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Tue Nov 29 09:10:03 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "https://www.pnas.org/doi/abs/10.1073/pnas.17.12.684", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/content/by/year", } @Article{Champernowne:1933:CDN, author = "D. G. Champernowne", title = "The construction of decimals normal in the scale of ten", journal = j-J-LOND-MATH-SOC, volume = "8", number = "4", pages = "254--260", month = "????", year = "1933", CODEN = "JLMSAK", DOI = "https://doi.org/10.1112/jlms/s1-8.4.254", ISSN = "0024-6107 (print), 1469-7750 (electronic)", ISSN-L = "0024-6107", bibdate = "Wed Dec 21 06:41:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the London Mathematical Society", journal-URL = "http://jlms.oxfordjournals.org/content/by/year", remark = "``Normal numbers'' are those whose digits are random in some specified base. This paper shows that the number $ .123456789101112 \ldots {} $ formed by the juxtaposition of consequence integers is normal in base ten.", } @Article{Glivenko:1933:SDE, author = "V. I. Glivenko", title = "Sulla determinazione empirica delle leggi di probabilit{\`a}. ({Italian}) [{On} the empirical determination of a probability law]", journal = "Giornale dell'Istituto Italiano degli Attuari", volume = "4", number = "??", pages = "92--99", month = "????", year = "1933", CODEN = "????", ISSN = "0390-5780", bibdate = "Wed Jan 18 08:25:59 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Italian", } @Article{Kolmogorov:1933:SDE, author = "Andrei Nikolaevich Kolmogorov", title = "Sulla Determinazione Empirica di una Legge di Distributione. ({Italian}) [{On} the empirical determination of a distribution law]", journal = "Giornale dell'Istituto Italiano degli Attuari", volume = "4", number = "??", pages = "83--91", month = "????", year = "1933", CODEN = "????", ISSN = "0390-5780", bibdate = "Tue Jan 17 21:35:06 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Italian", remark = "This paper, together with \cite{Smirnov:1939:OUE}, is the origin of the Kolmogorov--Smirnov test for goodness of fit.", xxpages = "1--11", } @Article{Mahalanobis:1934:TRS, author = "P. C. Mahalanobis", title = "Tables of random samples from a normal population", journal = j-SANKHYA-A, volume = "1", number = "2--3", pages = "289--328", month = may, year = "1934", CODEN = "SNKYA5", ISSN = "0036-4452", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "With the cooperation of Subhendu Sekhar Bose, Prabhat Ranjan Ray, and Sudhir Kumar Banerji.", URL = "http://www.jstor.org/stable/40383681", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", HDnumber = "73", } @Article{Pearson:1934:NMD, author = "Karl Pearson", title = "On a New Method of Determining {``Goodness} of Fit''", journal = j-BIOMETRIKA, volume = "26", number = "4", pages = "425--442", month = dec, year = "1934", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2331988", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 14:32:13 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315388; https://www.math.utah.edu/pub/tex/bib/biometrika1930.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "According to \cite[page 36]{Teichroew:1965:HDS}, this paper introduced the $ P_n(\lambda) $ test for ``determining whether a sample of size $n$, supposed to have been drawn at random from a parent population having a known probability integral has probably been drawn at random.'' See \cite{Nair:1938:TRS} for its first use on random numbers from a uniform distribution.", URL = "http://www.jstor.org/stable/2331988", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://www.jstor.org/journals/00063444.html", } @Article{Working:1934:RDS, author = "Holbrook Working", title = "A random-difference series for use in the analysis of time series", journal = j-J-AM-STAT-ASSOC, volume = "29", number = "185", pages = "11--24", month = mar, year = "1934", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Jan 16 14:53:22 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2278456", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", remark = "The random difference series in this paper are derived from Tippett's random numbers \cite{Tippett:1927:RSN}.", } @Book{Kadyrov:1936:TRN, author = "M. Kadyrov", title = "Tables of random numbers", publisher = "Izdat. Sredne-Aziatkogo Gos. Univ.", address = "Ta{\v{s}}kent, USSR", pages = "????", year = "1936", LCCN = "????", bibdate = "Thu Jan 19 07:00:14 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Russian", } @Article{Kermack:1937:SDA, author = "W. O. Kermack and A. G. McKendrick", title = "Some distributions associated with a randomly arranged set of numbers", journal = j-PROC-R-SOC-EDINB, volume = "57", number = "??", pages = "332--376", year = "1937", CODEN = "PRSEAE", ISSN = "0080-4541 (print), 2053-5902 (electronic)", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society of Edinburgh", HDnumber = "65", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PRE", } @Article{Kermack:1937:TRS, author = "W. O. Kermack and A. G. McKendrick", title = "Tests for randomness in a series of numerical observations", journal = j-PROC-R-SOC-EDINB, volume = "57", number = "??", pages = "228--240", year = "1937", CODEN = "PRSEAE", ISSN = "0080-4541 (print), 2053-5902 (electronic)", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society of Edinburgh", HDnumber = "64", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PRE", remark = "This paper tests Tippett's random numbers \cite{Tippett:1927:RSN}.", } @Book{Fisher:1938:STB, author = "Ronald Aylmer Fisher and Frank Yates", title = "Statistical Tables for Biological, Agricultural and Medical Research", publisher = pub-OLIVER-BOYD, address = pub-OLIVER-BOYD:adr, pages = "viii + 90 + 1", year = "1938", LCCN = "HA33 .F53", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July 1962)", remark = "First edition; see also 2nd (1943) to 6th (1963) editions. This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc", xxaddress = "Harlow, Essex, UK", xxpublisher = "Longman", } @Article{Hey:1938:NME, author = "G. B. Hey", title = "A New Method of Experimental Sampling Illustrated on Certain Non-Normal Populations", journal = j-BIOMETRIKA, volume = "30", number = "1/2", pages = "68--80", month = jun, year = "1938", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2332225", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 14:32:18 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315396; https://www.math.utah.edu/pub/tex/bib/biometrika1930.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2332225", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", remark = "According to \cite[page 37]{Teichroew:1965:HDS}, this paper was the first to ask the question ``How much sampling must be done to reduce the error due to sampling fluctuations?''.", } @Article{Kendall:1938:RRS, author = "M. G. Kendall and B. Babington-Smith", title = "Randomness and random sampling numbers", journal = j-J-R-STAT-SOC, volume = "101", number = "??", pages = "147--166", year = "1938", CODEN = "????", ISSN = "0952-8385", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "J. Roy. Stat. Soc.", fjournal = "Journal of the Royal Statistical Society", HDnumber = "61", journal-URL = "http://www.jstor.org/journals/09528385.html", } @Article{Lehmer:1938:PSE, author = "D. H. Lehmer", title = "Problems and Solutions: Elementary Problems: Solutions: {Euclid}'s Algorithm for Large Numbers", journal = j-AMER-MATH-MONTHLY, volume = "45", number = "4", pages = "227--233", month = apr, year = "1938", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:53 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Nair:1938:TRS, author = "K. N. Nair", title = "On {Tippett}'s random sampling numbers", journal = j-SANKHYA-A, volume = "4", number = "1", pages = "65--72", year = "1938", CODEN = "SNKYA5", ISSN = "0036-4452", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/40383888", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", HDnumber = "89", } @Article{Yule:1938:TTR, author = "G. Udny Yule", title = "A test of {Tippett}'s random sampling numbers", journal = j-J-R-STAT-SOC, volume = "101", number = "1", pages = "167--172", year = "1938", CODEN = "????", ISSN = "0952-8385", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2980656", acknowledgement = ack-nhfb, ajournal = "J. Roy. Stat. Soc.", fjournal = "Journal of the Royal Statistical Society", HDnumber = "142", journal-URL = "http://www.jstor.org/journals/09528385.html", } @Article{Dietze:1939:CCN, author = "E. Dietze and W. D. {Goodale, Jr.}", title = "The Computation of the Composite Noise Resulting from Random Variable Sources", journal = j-BELL-SYST-TECH-J, volume = "18", number = "4", pages = "605--623", month = oct, year = "1939", CODEN = "BSTJAN", ISSN = "0005-8580", bibdate = "Tue Nov 9 11:15:53 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1939/BSTJ.1939.1804.html; http://www.alcatel-lucent.com/bstj/vol18-1939/bstj-vol18-issue04.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol18/bstj18-4-605.pdf; http://www.alcatel-lucent.com/bstj/vol18-1939/articles/bstj18-4-605.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Kendall:1939:SPR, author = "M. G. Kendall and B. Babington-Smith", title = "Second paper on random sampling numbers", journal = "J. Roy. Stat. Soc., Supplement", volume = "6", number = "1", pages = "51--61", month = "????", year = "1939", CODEN = "????", ISSN = "1466-6162", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2983623", acknowledgement = ack-nhfb, ajournal = "J. Roy. Stat. Soc., Supplement", fjournal = "Supplement to the Journal of the Royal Statistical Society", HDnumber = "62", } @Book{Kendall:1939:TRS, author = "Maurice G. (Maurice George) Kendall and Bernard Babington-Smith", title = "Tables of random sampling numbers", volume = "24", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "x + 60", year = "1939", LCCN = "QA47 .T7 no.24", bibdate = "Mon Jun 27 15:04:05 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "Tracts for Computers", acknowledgement = ack-nhfb, author-dates = "1907--1983", HDnumber = "63", remark-1 = "On cover: Department of Statistics. University of London, University College.", remark-2 = "See \cite{Wold:1948:RND} for a transformation to normally-distributed random numbers.", subject = "Sampling (Statistics); Mathematics; Tables", } @Article{Mahler:1939:UKK, author = "Kurt Mahler", title = "{Ein {\"U}bertragungsprinzip f{\"u}r konvexe K{\"o}rper}. ({German}) [{A} theorem on transfer for convex bodies]", journal = "{\v{C}}asopis pro p{\v{e}}stov{\'a}n{\'\i} matematiky a fysiky", volume = "68", number = "3--4", pages = "93--102", month = "????", year = "1939", CODEN = "????", ISSN = "0528-2195", MRnumber = "MR 0001242", bibdate = "Mon Dec 26 11:20:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://dml.cz/dmlcz/109441", ZMnumber = "65.0175.02; 0021.10403", acknowledgement = ack-nhfb, ajournal = "{\v{C}}asopis Mat. Fysik., Praha", language = "German", remark = "Incompletely cited in \cite{Ripley:1983:LSP} as a source of part of a proof on lattice hyperplane spacing.", xxISSN = "1802-114X", } @Article{Smirnov:1939:EDB, author = "N. Smirnov", title = "On the estimation of the discrepancy between empirical curves of distribution for two independent samples", journal = "Bulletin Math{\'e}matique de l'Universit{\'e} de {Moscou}, S{\'e}rie internationale 2", volume = "2", number = "2", pages = "1--16", month = "????", year = "1939", CODEN = "????", ISSN = "????", MRclass = "62.0X", MRnumber = "MR0002062 (1,345f)", bibdate = "Wed Jan 18 08:29:59 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "Zbl 0023.24902", acknowledgement = ack-nhfb, fjournal = "Bulletin de l'Universit{\'e} d'{\'e}tat {\'a} {Moscou}. S{\'e}rie internationale. Section A: Math{\'e}matiques et m{\'e}canique", pagecount = "16", xxauthor = "V. I. Smirnov", } @Article{Smirnov:1939:OUE, author = "N. V. Smirnov", title = "Ob uklonenijah empiri{\v{c}}eskoi krivoi raspredelenija. ({Russian}). [Sur les {\'e}carts de la courbe de distribution empirique. ({French})] [{On} deviations from the empirical distribution curve]", journal = "Recueil Math{\'e}matique (Matemati{\v{c}}eski{\u\i} Sbornik), {N.S.}", volume = "6", number = "48", pages = "3--26", month = "????", year = "1939", CODEN = "MATSAB", ISSN = "0368-8666", MRclass = "60.0X", MRnumber = "MR0001483 (1,246b)", bibdate = "Tue Jan 17 21:38:41 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Matematicheski{\u\i} sbornik / izdavaemy{\u\i} Moskovskim matematicheskim obshchestvom = Recueil math{\'e}matique de la Soci{\'e}t{\'e} math{\'e}matique de Moscou", language = "Russian and French", remark = "This paper, in Russian with a French summary, together with \cite{Kolmogorov:1933:SDE}, is the origin of the Kolmogorov--Smirnov test for goodness of fit.", } @Article{Vickery:1939:DRS, author = "C. W. Vickery", title = "On drawing a random sample from a set of punched cards", journal = "J. Roy. Stat. Soc., Supplement", volume = "6", number = "1", pages = "62--66", year = "1939", CODEN = "????", ISSN = "1466-6162", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2983624", acknowledgement = ack-nhfb, ajournal = "J. Roy. Stat. Soc., Supplement", fjournal = "Supplement to the Journal of the Royal Statistical Society", HDnumber = "131", } @Article{Church:1940:CRS, author = "A. Church", title = "On the concept of a random sequence", journal = j-BULL-AMS, volume = "46", number = "??", pages = "130--135", month = "????", year = "1940", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Mon Jan 16 22:55:41 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @Article{Kendall:1941:TR, author = "M. G. Kendall", title = "A Theory of Randomness", journal = j-BIOMETRIKA, volume = "32", number = "1", pages = "1--15", month = jan, year = "1941", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2332245", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 14:32:23 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315397; https://www.math.utah.edu/pub/tex/bib/biometrika1940.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2332245", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", } @Article{Kolmogoroff:1941:CLU, author = "A. Kolmogoroff", title = "Confidence limits for an unknown distribution function", journal = j-ANN-MATH-STAT, volume = "12", number = "4", pages = "461--463", month = dec, year = "1941", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Wed Jan 18 08:22:52 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2235958", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Nair:1941:DSC, author = "A. N. K. Nair", title = "Distribution of {Student}'s '$t$' and the correlation coefficient in samples from non-normal populations", journal = j-SANKHYA-A, volume = "5", number = "??", pages = "383--400", month = "????", year = "1941", CODEN = "SANABS", ISSN = "0036-4452", bibdate = "Mon Jan 16 14:46:35 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", } @Article{Young:1941:ROS, author = "L. C. Young", title = "On randomness in ordered sequences", journal = j-ANN-MATH-STAT, volume = "12", number = "3", pages = "293--300", month = sep, year = "1941", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jan 16 22:55:07 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2235858", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Dodd:1942:CTR, author = "Edward L. Dodd", title = "Certain tests for randomness applied to data grouped into small sets", journal = j-ECONOMETRICA, volume = "10", number = "??", pages = "249--257", month = "????", year = "1942", CODEN = "ECMTA7", ISSN = "0012-9682", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Econometrica", HDnumber = "22", journal-URL = "http://www.jstor.org/journal/econometrica", remark = "This paper tests Tippett's random numbers \cite{Tippett:1927:RSN}.", } @Article{Dodd:1942:TTR, author = "Edward L. Dodd", title = "A transformation of {Tippett} random sampling numbers into numbers normally distributed", journal = "Bolet{\'\i}n de Matem{\'a}ticas", volume = "15", number = "??", pages = "73--77", month = "????", year = "1942", CODEN = "BOMAD4", ISSN = "0120-0380", MRclass = "62.0X", MRnumber = "MR0008668 (5,43b)", bibdate = "Mon Jan 16 14:22:26 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, xxjournal = "Bolletin Matim{\'a}tico", } @Article{Mann:1942:CNC, author = "H. B. Mann and A. Wald", title = "On the Choice of the Number of Class Intervals in the Application of the Chi Square Test", journal = j-ANN-MATH-STAT, volume = "13", number = "3", pages = "306--317", month = sep, year = "1942", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177731569", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Sat May 31 09:10:28 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/annmathstat.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177731569; http://www.jstor.org/stable/2235942", ZMnumber = "Zbl 0063.03772", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Peatman:1942:TRN, author = "J. G. Peatman and R. Shafer", title = "A table of random numbers from {Selective Service} numbers", journal = j-J-PSYCHOL, volume = "14", number = "??", pages = "295--305", month = "????", year = "1942", CODEN = "JOPSAM", ISSN = "0022-3980 (print), 1940-1019 (electronic)", ISSN-L = "0022-3980", bibdate = "Mon Jan 16 14:48:16 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Psychology", } @Article{Rosander:1942:UIT, author = "A. C. Rosander", title = "The use of inversions as a test of random order", journal = j-J-AM-STAT-ASSOC, volume = "37", number = "219", pages = "352--358", month = sep, year = "1942", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2279003", acknowledgement = ack-nhfb, ajournal = "J. Amer. Stat. Assoc.", fjournal = "Journal of the American Statistical Association", HDnumber = "106", journal-URL = "http://www.tandfonline.com/loi/uasa20", remark = "This paper tests Tippett's random numbers \cite{Tippett:1927:RSN}.", } @Book{Fisher:1943:STB, author = "Sir Ronald Aylmer Fisher and Frank Yates", title = "Statistical tables for biological, agricultural, and medical research", publisher = pub-OLIVER-BOYD, address = pub-OLIVER-BOYD:adr, edition = "Second", pages = "98", year = "1943", LCCN = "HA33 .F53 1943", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (1890--1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc", } @Article{Forsythe:1943:CSI, author = "G. E. Forsythe", title = "{Ces{\`a}ro} summability of independent random variables", journal = j-DUKE-MATH-J, volume = "10", number = "??", pages = "397--428", year = "1943", CODEN = "DUMJAO", DOI = "https://doi.org/10.1215/S0012-7094-43-01034-8", ISSN = "0012-7094 (print), 1547-7398 (electronic)", ISSN-L = "0012-7094", bibdate = "Tue Nov 22 09:08:17 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.dmj/1077471948", ZMnumber = "0063.01410", acknowledgement = ack-nhfb, fjournal = "Duke Mathematical Journal", journal-URL = "http://projecteuclid.org/info/euclid.dmj", } @Article{Gage:1943:CTR, author = "Robert Gage", title = "Contents of {Tippett}'s {``Random Sampling Numbers''}", journal = j-J-AM-STAT-ASSOC, volume = "38", number = "222", pages = "223--227", month = jun, year = "1943", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 06:10:35 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314101; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2279542", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", HDnumber = "32", journal-URL = "http://www.tandfonline.com/loi/uasa20", remark = "This paper tests Tippett's random numbers \cite{Tippett:1927:RSN}.", } @Article{Swed:1943:TTR, author = "Frieda S. Swed and C. Eisenhart", title = "Tables for testing randomness of grouping in a sequence of alternatives", journal = j-ANN-MATH-STAT, volume = "14", number = "1", pages = "66--87", month = mar, year = "1943", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177731494; http://www.jstor.org/stable/2236004", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "117", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Wald:1943:ETR, author = "A. Wald and J. Wolfowitz", title = "An exact test for randomness in the non-parametric case, based on serial correlation", journal = j-ANN-MATH-STAT, volume = "14", number = "4", pages = "378--388", month = dec, year = "1943", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jan 16 22:54:15 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2235925", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Dixon:1944:FCP, author = "W. J. Dixon", title = "Further Contributions to the Problem of Serial Correlation", journal = j-ANN-MATH-STAT, volume = "15", number = "2", pages = "119--144", month = jun, year = "1944", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Tue Jan 31 12:08:34 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236194", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Levene:1944:CMR, author = "H. Levene and J. Wolfowitz", title = "The covariance matrix of runs up and down", journal = j-ANN-MATH-STAT, volume = "15", number = "1", pages = "58--69", month = mar, year = "1944", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177731314", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177731314; http://www.jstor.org/stable/2236211", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "70", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Onsager:1944:CST, author = "Lars Onsager", title = "Crystal Statistics. {I}. {A} Two-Dimensional Model with an Order-Disorder Transition", journal = j-PHYS-REV, volume = "65", number = "3--4", pages = "117--149", month = feb, year = "1944", CODEN = "PHRVAO", DOI = "https://doi.org/10.1103/PhysRev.65.117", ISSN = "0031-899X (print), 1536-6065 (electronic)", ISSN-L = "0031-899X", bibdate = "Thu Feb 16 18:18:27 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://link.aps.org/doi/10.1103/PhysRev.65.117", acknowledgement = ack-nhfb, fjournal = "Physical Review", journal-URL = "http://pra.aps.org/browse", remark = "This is the famous paper in which Osager (winner of the 1968 Nobel Prize in Chemistry) derives an exact solution for the two-dimensional Ising lattice, a problem that is often used in testing of random-number generators for use in Monte Carlo simulations in physics.", } @Article{Rice:1944:MAR, author = "S. O. Rice", title = "Mathematical Analysis of Random Noise", journal = j-BELL-SYST-TECH-J, volume = "23", number = "3", pages = "282--332", month = jul, year = "1944", CODEN = "BSTJAN", ISSN = "0005-8580", MRclass = "60.0X", MRnumber = "0010932 (6,89b)", MRreviewer = "M. Kac", bibdate = "Tue Nov 9 11:15:53 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1944/BSTJ.1944.2303.html; http://www.alcatel-lucent.com/bstj/vol23-1944/bstj-vol23-issue03.html; https://www.math.utah.edu/pub/tex/bib/bstj1940.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol23/bstj23-3-282.pdf; http://www.alcatel-lucent.com/bstj/vol23-1944/articles/bstj23-3-282.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Wolfowitz:1944:ADR, author = "J. Wolfowitz", title = "Asymptotic distribution of runs up and down", journal = j-ANN-MATH-STAT, volume = "15", number = "2", pages = "163--172", month = jun, year = "1944", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jan 16 22:53:44 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236196", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Rice:1945:MAR, author = "S. O. Rice", title = "Mathematical Analysis of Random Noise", journal = j-BELL-SYST-TECH-J, volume = "24", number = "1", pages = "46--156", month = jan, year = "1945", CODEN = "BSTJAN", ISSN = "0005-8580", MRclass = "60.0X", MRnumber = "0011918 (6,233i)", MRreviewer = "M. Kac", bibdate = "Tue Nov 9 11:15:54 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1945/BSTJ.1945.2401.html; http://www.alcatel-lucent.com/bstj/vol24-1945/bstj-vol24-issue01.html; https://www.math.utah.edu/pub/tex/bib/bstj1940.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol24/bstj24-1-46.pdf; http://www.alcatel-lucent.com/bstj/vol24-1945/articles/bstj24-1-46.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Copeland:1946:NNN, author = "A. H. Copeland and P. Erd{\H{o}}s", title = "Note on normal numbers", journal = j-BULL-AMS, volume = "52", number = "??", pages = "857--860", month = "????", year = "1946", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Wed Dec 21 06:39:20 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", remark = "``Normal numbers'' are those whose digits are random in some specified base.", } @Article{Olmstead:1946:DSA, author = "P. S. Olmstead", title = "Distribution of sample arrangements for runs up and down", journal = j-ANN-MATH-STAT, volume = "17", number = "1", pages = "24--33", month = mar, year = "1946", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jan 16 22:52:52 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2235901", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Forsythe:1947:NSR, author = "George E. Forsythe", title = "On {N{\"o}rlund} summability of random variables to zero", journal = j-BULL-AMS, volume = "53", number = "??", pages = "302--313", year = "1947", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", MRclass = "60.0X", MRnumber = "MR0020738 (8,591b)", MRreviewer = "M. Kac", bibdate = "Tue Nov 22 09:08:17 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.bams/1183510599", ZMnumber = "0037.08105", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", keywords = "Probability theory", } @Article{Moran:1947:RDI, author = "P. A. P. Moran", title = "The random division of an interval", journal = "J. Roy. Stat. Soc., Supplement", volume = "9", number = "??", pages = "92--98", month = "????", year = "1947", ISSN = "1466-6162", bibdate = "Wed Feb 08 19:06:50 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Ulam:1947:CSD, author = "S. M. Ulam and John von Neumann", title = "On combinations of stochastic and deterministic processes", journal = j-BULL-AMS, volume = "53", number = "11", pages = "1120--1120", month = nov, year = "1947", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Mon Jun 06 19:17:03 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/nld.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "The abstract notes ``\ldots{} starting with almost every $ x_1 $ (in the sense of Lebesgue measure) and {\em iterating\/} the function $ f(x) = 4 \cdot (1 - x) $ one obtains a sequence of numbers on $ (0, 1) $ with a computable algebraic distribution. By playing suitable games with numbers `drawn' in this fashion, one can obtain various other distributions, either given explicitly or satisfying given differential or integral equations.''", URL = "http://www.ams.org/journals/bull/1947-53-11/S0002-9904-1947-08918-7/S0002-9904-1947-08918-7.pdf", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", keywords = "logistic map, deterministic model, stochastic model", received = "3 September 1947", remark = "One-paragraph abstract.", } @TechReport{Brown:1948:STR, author = "Bernice Brown", title = "Some Tests of the Randomness of a Million Digits", type = "Report", number = "RAND RAOP-44", institution = "RAND Corporation", address = "Santa Monica, CA, USA", pages = "????", year = "1948", bibdate = "Tue Sep 20 07:20:22 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, remark = "This report is about the RAND million-random-digit corpus.", } @Article{Feller:1948:KSL, author = "W. Feller", title = "On {the Kolmogorov--Smirnov} limit theorems for empirical distributions", journal = j-ANN-MATH-STAT, volume = "19", number = "2", pages = "177--189", month = jun, year = "1948", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Wed Jan 18 08:58:13 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236265", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Hamaker:1948:RFE, author = "H. C. Hamaker", title = "Random frequencies, expedient for the construction of artificial samples of large size", journal = "Statistica Rijswijk", volume = "2", number = "??", pages = "129--137", month = "????", year = "1948", CODEN = "????", ISSN = "????", bibdate = "Mon Jan 16 14:27:40 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, xxnote = "I cannot find this journal in any of dozens of library catalogs.", } @Article{Hamaker:1948:RSN, author = "H. C. Hamaker", title = "Random sampling numbers", journal = "Statistica Rijswijk", volume = "2", number = "??", pages = "97--106", month = "????", year = "1948", CODEN = "????", ISSN = "????", bibdate = "Mon Jan 16 14:27:40 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, xxnote = "I cannot find this journal in any of dozens of library catalogs.", } @Article{Horton:1948:MOR, author = "H. Burke Horton", title = "A method for obtaining random numbers", journal = j-ANN-MATH-STAT, volume = "19", number = "1", pages = "81--85", month = mar, year = "1948", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177730294", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Sat Sep 17 10:12:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236060", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "52", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Book{Ore:1948:NTH, author = "{\O}ystein {\O}re", title = "Number theory and its history", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "x + 370", year = "1948", LCCN = "QA241 .O7", bibdate = "Mon Jun 27 15:30:25 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1899--1968", HDnumber = "92", subject = "Number theory; Mathematics; History", } @Article{Smirnov:1948:TEG, author = "N. Smirnov", title = "Tables for Estimating the Goodness of Fit of Empirical Distributions", journal = j-ANN-MATH-STAT, volume = "19", number = "2", pages = "279--281", month = jun, year = "1948", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "62.0X", MRnumber = "MR0025109 (9,599j)", bibdate = "Tue Jan 17 21:52:06 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236278", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", remark = "Reproduction of tables from \cite{Smirnov:1939:EDB}.", } @Book{Wold:1948:RND, author = "Herman O. A. Wold and Maurice G. (Maurice George) Kendall", title = "Random normal deviates: 25,000 items compiled from Tract no. {XXIV} {(M. G. Kendall and B. Babington-Smith's Tables of random sampling numbers)}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xiii + 51", year = "1948", LCCN = "QA47 .T7 no.25", bibdate = "Mon Jun 27 16:30:11 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; library.ox.ac.uk:210/ADVANCE", note = "See \cite{Kendall:1939:TRS}.", acknowledgement = ack-nhfb, author-dates = "Herman O. A. Wold (1908--1992); Maurice G. (Maurice George) Kendall (1907--1983)", HDnumber = "141", subject = "Sampling (Statistics); Mathematics; Tables", } @TechReport{Brown:1949:HRR, author = "George W. Brown", title = "History of {RAND}'s random digits---summary", type = "Report", number = "P-113", institution = "RAND Corporation", address = "Santa Monica, CA, USA", pages = "6", month = jun, year = "1949", bibdate = "Tue Sep 20 07:57:17 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.rand.org/pubs/papers/2008/P113.pdf", acknowledgement = ack-nhfb, remark = "This report describes how the RAND corpus of a million random digits \cite{RAND:1955:MRD} was initially produced from an electronic simulation of a roulette wheel. When chi-squared tests suggested a slight lack of randomness, the 20,000 punched cards, each with 50 random decimal digits, were reprocessed. From page 4 of the original technical report: ``We added (mod 10) the digits in each card, digit by digit, to the corresponding digits of the previous card. The derived table of one million digits was then subjected to the various standard tests, frequency tests, serial tests, poker tests, etc. These million digits have a clean bill of health and have been adopted as RAND's table of random digits.''", } @Article{Doob:1949:HAK, author = "J. L. Doob", title = "Heuristic Approach to the {Kolmogorov--Smirnov} Theorems", journal = j-ANN-MATH-STAT, volume = "20", number = "3", pages = "393--403", month = sep, year = "1949", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Tue Jan 17 21:51:00 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236535", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Book{Fisher:1949:STB, author = "Sir Ronald Aylmer Fisher and Frank Yates", title = "Statistical tables for biological, agricultural, and medical research", publisher = "Hafner Pub. Co.", address = "New York", edition = "Third", pages = "viii + 112", year = "1949", LCCN = "HA33 .F53 1949", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (1890--1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc", } @Article{Hamaker:1949:RSF, author = "H. C. Hamaker", title = "Random sampling frequencies: an implement for rapidly constructing large-size artificial samples", journal = "Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen", volume = "52", number = "??", pages = "432--439", month = "????", year = "1949", CODEN = "PKNAAU", ISSN = "0370-0348", bibdate = "Mon Jan 16 14:30:51 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Hamaker:1949:STP, author = "H. C. Hamaker", title = "A simple technique for producing random sampling numbers", journal = "Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen", volume = "52", number = "??", pages = "145--150", year = "1949", CODEN = "PKNAAU", ISSN = "0370-0348", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Nederl. Akad. Wetensch. Proc.", HDnumber = "48", } @Article{Horton:1949:DMP, author = "H. Burke Horton and R. Tynes {Smith III}", title = "A direct method for producing random digits in any number system", journal = j-ANN-MATH-STAT, volume = "20", number = "1", pages = "82--90", month = mar, year = "1949", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177730092", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236805", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "53", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @TechReport{Mauchly:1949:PRN, author = "J. W. Mauchly", title = "Pseudo-random numbers", type = "Report", number = "??", institution = "Eckert-Mauchly Computer Corporation", address = "????", year = "1949", bibdate = "Mon Jun 27 15:21:18 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "81", } @Article{Metropolis:1949:MCM, author = "Nicholas Metropolis and S. Ulam", title = "The {Monte Carlo} method", journal = j-J-AM-STAT-ASSOC, volume = "44", number = "247", pages = "335--341", month = sep, year = "1949", CODEN = "JSTNAL", DOI = "https://doi.org/10.2307/2280232", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "65.0X", MRnumber = "MR0031341 (11,138c)", MRreviewer = "J. L. Doob", bibdate = "Tue Nov 5 08:02:08 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2280232", ZMnumber = "0033.28807", acknowledgement = ack-nhfb, annote = "This is one of the earliest published articles on the Monte Carlo method; see \cite{Hurd:1985:NEM}.", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", keywords = "ENIAC; probability theory", } @Book{Stevens:1949:TRD, author = "W. H. S. Stevens", title = "Table of 105,000 random decimal digits", volume = "4914", publisher = "Interstate Commerce Commission", address = "Washington, DC, USA", year = "1949", LCCN = "QA276.5 .U5 1949", bibdate = "Sat Jan 7 12:05:57 MST 2012", bibsource = "catalog.princeton.edu:7090/voyager; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, subject = "sampling (statistics); statistics; graphic methods", } @Article{Walsh:1949:CCR, author = "John E. Walsh", title = "Concerning compound randomization in the binary system", journal = j-ANN-MATH-STAT, volume = "20", number = "4", pages = "580--589", month = dec, year = "1949", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177729950", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177729950; http://www.jstor.org/stable/2236313", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "137", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @InProceedings{Eisenhart:1950:RDD, author = "C. Eisenhart and L. S. Deming", booktitle = "{National Bureau of Standards Seminar, February 17, Washington, DC}", title = "On the randomness of the digits of $ \pi $ and $e$ to 2000 decimal places", publisher = "????", address = "????", pages = "??--??", year = "1950", bibdate = "Mon Jan 16 14:24:10 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/pi.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Book{Good:1950:PWE, author = "Irving John Good", title = "Probability and the weighing of evidence", publisher = "C. Griffin", address = "London, UK", pages = "viii + 119", year = "1950", LCCN = "QA273 .G65", bibdate = "Sat Jan 7 11:03:33 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, remark = "From \cite[page 43]{Good:1969:HRR}, the author reports: ``If two random sequences are thus combined [by adding modulo a small number] the result will be flatter than either of them, so the device is useful for improving the quality of random digits. The theory behind this remark was submitted by the writer in 1946 to the Proc. Cambridge Phil. Soc. It was rejected on the grounds that the device of adding digits in order to make them more random was useless since `there are other and more satisfactory methods of producing random numbers'. This `useless' idea has since been used by RAND, as mentioned above, and by ERNIE, by SWAC [9], etcetera, etcetera, etcetera. Referees are fallible like people. The theory was published as an exercise in \cite[page 58]{Good:1950:PWE}\ldots{}''.", subject = "Probabilities", tableofcontents = "Theories of probability \\ The origin of the axioms \\ The abstract theory \\ The theory and technique of probability \\ Probability distributions \\ Weighing evidence \\ Statistics and probability \\ Appendices: I. The error function \\ II. Dirichlet's multiple integral \\ III. On the conventionality of the addition and product laws", } @Article{Gruenberger:1950:TRD, author = "Fred Gruenberger", title = "Tests of random digits", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "4", number = "32", pages = "244--245", year = "1950", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "45", journal-URL = "http://www.ams.org/mcom/", } @Article{Kac:1950:DMP, author = "Mark Kac and Harry Pollard", title = "The distribution of the maximum of partial sums of independent random variables", journal = j-CAN-J-MATH, volume = "2", number = "??", pages = "375--384", month = "????", year = "1950", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1950-034-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "60.0X", MRnumber = "0036465 (12,114b)", MRreviewer = "M. Lo{\`e}ve", bibdate = "Sat Sep 10 15:38:24 MDT 2011", bibsource = "http://cms.math.ca/cjm/v2/; https://www.math.utah.edu/pub/tex/bib/canjmath.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Korobov:1950:SQU, author = "N. M. Korobov", title = "On some questions of uniform distribution", journal = "Izv. Akad. Nauk SSSR", volume = "14", number = "3", pages = "215--238", month = "????", year = "1950", CODEN = "????", ISSN = "????", bibdate = "Wed Jan 18 11:04:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Russian", } @Article{Massey:1950:NED, author = "Frank J. {Massey, Jr.}", title = "A Note on the Estimation of a Distribution Function by Confidence Limits", journal = j-ANN-MATH-STAT, volume = "21", number = "1", pages = "116--119", month = mar, year = "1950", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177729891", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Sat May 31 09:10:40 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/annmathstat.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177729891; http://www.jstor.org/stable/2236559", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", remark = "This paper contains a practical algorithm for computing the Kolmogorov--Smirnov probabilities for small sample sizes.", } @Article{Metropolis:1950:STV, author = "N. C. Metropolis and G. Reitwiesner and J. von Neumann", title = "Statistical treatment of values of first $ 2{,}000 $ decimal digits of $e$ and of $ \pi $ calculated on the {ENIAC}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "4", number = "30", pages = "109--111", year = "1950", CODEN = "MTTCAS", ISSN = "0891-6837", MRclass = "65.0X", MRnumber = "MR0037598 (12,286j)", MRreviewer = "R. P. Boas, Jr.", bibdate = "Mon Jun 06 19:17:03 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", abstract = "From the article: ``The first 2,000 decimal digits of $e$ and $ \pi $ were calculated on the ENIAC by Mr. G. Reitwiesner and several members of the ENIAC Branch of the Ballistic Research Laboratories at Aberdeen, Maryland \cite{Reitwiesner:1950:EDM}. A statistical survey of this material has failed to disclose an significant deviations from randomness for $ \pi $, but it has indicated quite serious ones for $e$.''", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", journal-URL = "http://www.ams.org/mcom/", remark = "Footnote to title: ``Both $e$ and $ 1 / e $ were computed somewhat beyond 2500\,D and the results checked by actual multiplication.''", } @Article{Williams:1950:CNW, author = "C. Arthur {Williams, Jr.}", title = "On the Choice of the Number and Width of Classes for the Chi-square Test for Goodness of Fit", journal = j-J-AM-STAT-ASSOC, volume = "45", number = "249", pages = "77--86", month = mar, year = "1950", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Tue Jan 17 21:54:47 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2280429", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @InCollection{Brown:1951:HRR, author = "George W. Brown", title = "History of {RAND}'s random digits---summary", crossref = "Householder:1951:MCM", pages = "31--32", year = "1951", bibdate = "Mon Jun 27 12:18:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "9", } @TechReport{Cameron:1951:MCE, author = "J. M. Cameron", title = "{Monte Carlo} experiments on {SEAC}", type = "Working Paper", number = "SEL-52-5", institution = pub-NBS, address = pub-NBS:adr, pages = "??", day = "27", month = oct, year = "1951", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "13", } @Article{Forsythe:1951:GTRa, author = "George E. Forsythe", title = "Generation and testing of random digits at the {National Bureau of Standards, Los Angeles}", journal = j-APPL-MATH-SER-NBS, volume = "12", number = "??", pages = "34--35", month = "????", year = "1951", CODEN = "????", ISSN = "1049-4685", bibdate = "Wed Jul 01 11:00:59 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Applied mathematics series / National Bureau of Standards", HDnumber = "30", } @Article{Forsythe:1951:GTRb, author = "George E. Forsythe", title = "Generation and testing of 1,217,370 `random' binary digits on the {SWAC}", journal = j-BULL-AMS, volume = "57", number = "??", pages = "304--304", month = "????", year = "1951", CODEN = "BAMOAD", ISSN = "0002-9904 (print), 1936-881X (electronic)", ISSN-L = "0002-9904", bibdate = "Mon Jun 27 13:41:27 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Abstract only.", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society", HDnumber = "29", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @Article{Gruenberger:1951:TRD, author = "Fred Gruenberger and A. M. Mark", title = "The $ d^2 $ test of random digits", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "5", number = "??", pages = "109--110", year = "1951", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "46", journal-URL = "http://www.ams.org/mcom/", } @InCollection{Hammer:1951:MSM, author = "Preston C. Hammer", booktitle = "{Monte Carlo} Method", title = "The mid-square method of generating digits", crossref = "Householder:1951:MCM", pages = "33--33", year = "1951", bibdate = "Mon Jun 27 12:18:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "49", } @Article{Kahn:1951:EPT, author = "Herman Kahn and T. E. Harris", title = "9. Estimation of particle transmission by random sampling", journal = "Journal of Research of the National Bureau of Standards. Applied Mathematics Series", volume = "12", number = "??", pages = "27--30", year = "1951", CODEN = "????", ISSN = "????", bibdate = "Wed Oct 02 17:53:08 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "https://dornsifecms.usc.edu/assets/sites/520/docs/kahnharris.pdf", acknowledgement = ack-nhfb, ajournal = "J. Research Nat. Bur. Stand., Appl. Math. Series", } @InProceedings{Lehmer:1951:MML, author = "D. H. Lehmer", title = "Mathematical methods in large-scale computing units", crossref = "Anonymous:1951:PSS", pages = "141--146", year = "1951", MRclass = "65.0X", MRnumber = "0044899 (13,495f)", MRreviewer = "R. Hamming", bibdate = "Tue Dec 21 16:17:16 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "The aim of this paper is to discuss in a general way certain features of the mathematics that are characteristic of the large scale digital computing machines. Special attention is given to the problem of generating random numbers. The author's proposal for generating a sequence of ``random'' 8 decimal numbers $ u_n $ is to start with some number $ u_0 \neq 0 $, multiply it by 23, and subtract the two digit overflow on the left from the two right hand digits to obtain a new number $ u_1 $. By repeating this process he generates a sequence $ u_n $ which he shows has a repetition period of 5,882,352. An IBM 602A was used to generate 5000 numbers of such a sequence. Four standard tests (unspecified) were applied to check the ``randomness'' and the sequence passed all four. The author observes, however, that all of the members of the sequence he chose were divisible by 17.", acknowledgement = ack-nhfb, HDnumber = "67", xxauthor = "D. H. (Derrick Henry) Lehmer", } @PhdThesis{Marsaglia:1951:SPC, author = "George Marsaglia", title = "Stochastic Processes and Classes of Random Variables", type = "{Ph.D.} thesis", school = "The Ohio State University", address = "Columbus, OH, USA", pages = "46", year = "1951", bibdate = "Wed Jun 22 07:10:43 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ezproxy.lib.utah.edu/docview/302068737?accountid=14677", acknowledgement = ack-nhfb, } @Article{Massey:1951:KST, author = "Frank J. {Massey, Jr.}", title = "The {Kolmogorov--Smirnov} test for goodness of fit", journal = j-J-AM-STAT-ASSOC, volume = "46", number = "253", pages = "68--78", month = mar, year = "1951", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Jan 16 14:40:03 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314132; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2280095", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @TechReport{Richtmyer:1951:EDI, author = "R. D. Richtmyer", title = "The evaluation of definite integrals, and a {Quasi-Monte-Carlo} method based on the properties of algebraic numbers", type = "Report", number = "LA-1342", institution = "Los Alamos Scientific Laboratory", address = "Los Alamos, NM, USA", year = "1951", bibdate = "Mon Jun 27 15:40:02 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "102", } @InProceedings{vonNeumann:1951:VTU, author = "John von Neumann", title = "13. {Various} techniques used in connection with random digits", crossref = "Householder:1951:MCM", pages = "36--38", year = "1951", bibdate = "Tue Jun 07 16:15:00 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Summary written by G. E. Forsythe. Reprinted in \cite[Paper 23, pp. 768--770]{Taub:1963:JNCa}.", URL = "https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf", acknowledgement = ack-nhfb, HDnumber = "133", remark = "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. [via enews]", } @Article{Votaw:1951:HSS, author = "D. F. {Votaw, Jr.} and J. A. Rafferty", title = "High Speed Sampling", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "5", number = "33", pages = "1--8", month = jan, year = "1951", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "134", journal-URL = "http://www.ams.org/mcom/", } @Article{Anderson:1952:ATC, author = "T. W. Anderson and D. A. Darling", title = "Asymptotic theory of certain `goodness of fit' criteria based on stochastic processes", journal = j-ANN-MATH-STAT, volume = "23", number = "2", pages = "193--212", month = jun, year = "1952", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177729437", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "62.0X", MRnumber = "0050238 (14,298h)", MRreviewer = "R. Fortet", bibdate = "Sat May 31 09:10:44 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/annmathstat.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177729437; http://www.jstor.org/stable/2236446", abstract = "The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $ F(x) $.", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Anonymous:1952:RD, author = "Anonymous", title = "Random Digits (1--6000)", journal = j-J-AM-STAT-ASSOC, volume = "47", number = "260", pages = "710--714", month = dec, year = "1952", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314139; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2280798", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Cameron:1952:RST, author = "J. M. Cameron", title = "Results of some tests of randomness on pseudo-random on numbers (preliminary report)", journal = j-ANN-MATH-STAT, volume = "23", number = "1", pages = "138--138", month = mar, year = "1952", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Abstract only.", URL = "http://www.jstor.org/stable/2236409", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "14", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", remark = "One-paragraph comment on the analysis of random numbers produced on the SEAC by Olga Taussky-Todd.", } @Article{Goodman:1952:EPSa, author = "A. W. Goodman and W. M. Zaring", title = "Elementary Problems and Solutions: Solutions: {Euclid}'s Algorithm and the Least-Remainder Algorithm", journal = j-AMER-MATH-MONTHLY, volume = "59", number = "3", pages = "156--159", month = mar, year = "1952", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:38 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/2308186", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Ore:1952:GCR, author = "{\O}ystein {\O}re", title = "The General {Chinese} Remainder Theorem", journal = j-AMER-MATH-MONTHLY, volume = "59", number = "6", pages = "365--370", month = jun # "\slash " # jul, year = "1952", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:45 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Book{Tippett:1952:RSN, author = "Leonard Henry Caleb Tippett", title = "Random sampling numbers", volume = "15", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "viii + 26", year = "1952", LCCN = "QA47 .T7 no. 15", bibdate = "Mon Jun 27 13:35:14 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "With a foreword by editor Karl Pearson.", series = "Tracts for computers", acknowledgement = ack-nhfb, HDnumber = "123", remark = "This is a reprint of \cite{Tippett:1927:RSN}.", subject = "Mathematics; Tables; Sampling (Statistics)", } @Article{Anonymous:1953:RDa, author = "Anonymous", title = "Random Digits (6001--6100)", journal = j-J-AM-STAT-ASSOC, volume = "48", number = "261", pages = "167--167", month = mar, year = "1953", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314140; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2280898", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Anonymous:1953:RDb, author = "Anonymous", title = "Random Digits (6501--6875)", journal = j-J-AM-STAT-ASSOC, volume = "48", number = "262", pages = "383--383", month = jun, year = "1953", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314141; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281306", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Anonymous:1953:RDc, author = "Anonymous", title = "Random Digits (6876--8125)", journal = j-J-AM-STAT-ASSOC, volume = "48", number = "263", pages = "672--672", month = sep, year = "1953", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314142; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281029", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Anonymous:1953:RDd, author = "Anonymous", title = "Random Digits (9001--13,750)", journal = j-J-AM-STAT-ASSOC, volume = "48", number = "264", pages = "931--934", month = dec, year = "1953", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314143; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281094", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Curtiss:1953:MCM, author = "J. H. Curtiss", title = "{``Monte Carlo''} methods for the iteration of linear operators", journal = j-J-MATH-PHYS, volume = "32", number = "??", pages = "209--232", month = "????", year = "1953", CODEN = "JMAPAQ", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", HDnumber = "20", journal-URL = "http://jmp.aip.org/", } @TechReport{Duparc:1953:RSI, author = "H. J. A. Duparc and C. G. Lekkerkerker and W. Peremans", title = "Reduced sequences of integers and pseudo-random numbers", type = "Report", number = "ZW 1953-002", institution = "Mathematisch Centrum", address = "Amsterdam, The Netherlands", year = "1953", bibdate = "Mon Jun 27 13:30:34 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "23", } @Book{Fisher:1953:STBa, author = "Sir Ronald Aylmer Fisher and Frank Yates", title = "Statistical tables for biological, agricultural and medical research", publisher = pub-OLIVER-BOYD, address = pub-OLIVER-BOYD:adr, edition = "Fourth", pages = "xi + 126", year = "1953", LCCN = "QA276 .F498 1953a", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (1890--1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc; Mathematical statistics", } @Book{Fisher:1953:STBb, author = "Sir Ronald Aylmer Fisher and Frank Yates", title = "Statistical tables for biological, agricultural, and medical research", publisher = "Hafner Pub. Co.", address = "New York, NY, USA", edition = "Fourth", pages = "126", year = "1953", LCCN = "QA276 .F498 1953", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (1890--1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc; Mathematical statistics", } @TechReport{Gilbert:1953:QRB, author = "E. N. Gilbert", title = "Quasi-random binary sequences", type = "Report", number = "MM-53-1400-42", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", day = "27", month = nov, year = "1953", bibdate = "Mon Jun 27 14:22:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "33", } @Article{Good:1953:STS, author = "I. J. Good", title = "The serial test for sampling numbers and other tests for randomness", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "49", number = "??", pages = "276--284", year = "1953", CODEN = "PCPSA4", ISSN = "0008-1981", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences", HDnumber = "38", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", } @TechReport{Juncosa:1953:RNG, author = "M. L. Juncosa", title = "Random number generation on the {BRL} high-speed computing machines", type = "Report", number = "855", institution = "Ballistic Research Laboratories", address = "Aberdeen Proving Ground, MD, USA", year = "1953", bibdate = "Mon Jun 27 14:57:13 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "58", } @Article{Metropolis:1953:ESC, author = "Nicholas Metropolis and Arianna W. Rosenbluth and Marshall N. Rosenbluth and Augusta H. Teller and Edward Teller", title = "Equation of State Calculations by Fast Computing Machines", journal = j-J-CHEM-PHYS, volume = "21", number = "6", pages = "1087--1092", month = jun, year = "1953", CODEN = "JCPSA6", DOI = "https://doi.org/10.1063/1.1699114", ISSN = "0021-9606 (print), 1089-7690 (electronic)", ISSN-L = "0021-9606", bibdate = "Thu Oct 6 14:28:25 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "This article introduces the Metropolis algorithm, which the journal {\em Computing in Science and Engineering\/} cited in the top 10 algorithms having the ``greatest influence on the development and practice of science and engineering in the 20th Century.'' See \cite{Balazs:2000:ONC,Beichl:2000:MA}, and the Hasting--Metropolis generalization in \cite{Hastings:1970:MCS}. See also \cite{Barker:1965:MCC,Peskun:1973:OMC,Hitchcock:2003:HMH}.", URL = "http://link.aip.org/link/doi/10.1063/1.1699114; http://pubs.acs.org/cgi-bin/chemport/version=1.0&coi=1:CAS:528:DyaG3sXltlKhsw%253D%253D&pissn=0095-2338&pyear=2005&&md5=2eba6ee7d50b361b924c3ff8efeda4b1", abstract = "A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the 2-D rigid sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to the four-term virial coefficient expansion.", acknowledgement = ack-nhfb, author-dates = "Edward Teller (1908--2003)", fjournal = "Journal of Chemical Physics", journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse", keywords = "Gibbs sampling; jrnl; Metropolis algorithm; Monte Carlo integration; Monte Carlo process; simulated annealing; stochastic search", LSnumber = "85", } @Article{Moore:1953:STR, author = "P. G. Moore", title = "A Sequential Test for Randomness", journal = j-BIOMETRIKA, volume = "40", number = "1/2", pages = "111--115", month = jun, year = "1953", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2333102", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", MRclass = "62.0X", MRnumber = "0055641 (14,1104a)", MRreviewer = "J. Kiefer", bibdate = "Sat Jun 21 14:32:41 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315420; https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2333102", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", } @Article{Peck:1953:UDA, author = "L. G. Peck", title = "On uniform distribution of algebraic numbers", journal = j-PROC-AM-MATH-SOC, volume = "4", number = "??", pages = "440--443", year = "1953", CODEN = "PAMYAR", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", HDnumber = "98", journal-URL = "http://www.ams.org/journals/proc", } @PhdThesis{Teichroew:1953:DSH, author = "Daniel Teichroew", title = "Distribution sampling with high speed computers", type = "{Ph.D.} dissertation", school = "North Carolina State College", address = "Chapel Hill, NC, USA", pages = "vi + 147", year = "1953", bibdate = "Mon Jun 27 17:31:44 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://search.lib.unc.edu/search?R=UNCb3222025", acknowledgement = ack-nhfb, HDnumber = "119", } @Article{Anonymous:1954:RDa, author = "Anonymous", title = "Random Digits (12,876--15,125)", journal = j-J-AM-STAT-ASSOC, volume = "49", number = "265", pages = "206--207", month = mar, year = "1954", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314144; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281062", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Anonymous:1954:RDb, author = "Anonymous", title = "Random Digits (15,126--17,375)", journal = j-J-AM-STAT-ASSOC, volume = "49", number = "266", pages = "410--411", month = jun, year = "1954", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:30 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314145; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2280958", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Anonymous:1954:RDc, author = "Anonymous", title = "Random Digits (17,376--20,875)", journal = j-J-AM-STAT-ASSOC, volume = "49", number = "267", pages = "682--684", month = sep, year = "1954", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:31 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314146; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281154", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Anonymous:1954:RDd, author = "Anonymous", title = "Random Digits (20,876--21,875)", journal = j-J-AM-STAT-ASSOC, volume = "49", number = "268", pages = "928--928", month = dec, year = "1954", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:31 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314147; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281560", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Bartholomew:1954:NUS, author = "D. J. Bartholomew", title = "Note on the Use of {Sherman}'s Statistic as a Test for Randomness", journal = j-BIOMETRIKA, volume = "41", number = "3/4", pages = "556--558", month = dec, year = "1954", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2332738", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", MRclass = "62.0X", MRnumber = "0065097 (16,383a)", bibdate = "Sat Jun 21 14:32:45 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315423; https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2332738", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", keywords = "random numbers", } @Article{Hammersley:1954:PMM, author = "J. M. Hammersley and K. W. Morton", title = "Poor Man's {Monte Carlo}", journal = j-J-R-STAT-SOC-SER-B-METHODOL, volume = "16", number = "??", pages = "23--28", month = "????", year = "1954", CODEN = "JSTBAJ", ISSN = "0035-9246", bibdate = "Sat Jan 07 11:54:30 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series B (Methodological)", journal-URL = "http://www.jstor.org/journals/00359246.html", } @Article{Lehmer:1954:DRN, author = "D. H. Lehmer", title = "Description of {``Random} number generation on the {BRL} high-speed computing machines''", journal = j-MATH-REV, volume = "15", number = "??", pages = "559--559", month = "????", year = "1954", CODEN = "MAREAR", ISSN = "0025-5629", bibdate = "Mon Jan 23 18:01:23 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Reviews", } @TechReport{Meyer:1954:GTR, author = "H. A. Meyer and L. S. Gephart and N. L. Rasmussen", title = "On the generation and testing of random digits", type = "WADC Technical Report", number = "54--55", institution = "Air Res. Dev. Command", address = "Wright-Patterson Air Force Base, OH, USA", year = "1954", bibdate = "Mon Jun 27 15:23:55 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "84", } @Article{Moshman:1954:GPR, author = "Jack Moshman", title = "The Generation of Pseudo-Random Numbers on a Decimal Calculator", journal = j-J-ACM, volume = "1", number = "2", pages = "88--91", month = apr, year = "1954", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/320772.320775", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Fri Nov 04 00:18:27 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", HDnumber = "85", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Page:1954:MCS, author = "E. S. Page", title = "The {Monte Carlo} solution of some integral equations", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "50", number = "??", pages = "414--425", year = "1954", CODEN = "PCPSA4", ISSN = "0008-1981", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences", HDnumber = "93", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP", } @Article{Rosenbluth:1954:FRM, author = "Marshall N. Rosenbluth and Arianna W. Rosenbluth", title = "Further results on {Monte Carlo} equations of state", journal = j-J-CHEM-PHYS, volume = "22", number = "5", pages = "881--884", month = may, year = "1954", CODEN = "JCPSA6", DOI = "https://doi.org/10.1063/1.1740207", ISSN = "0021-9606 (print), 1089-7690 (electronic)", ISSN-L = "0021-9606", bibdate = "Sun Jun 23 19:07:39 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://scienze-como.uninsubria.it/bressanini/montecarlo-history/rosenbluth-1954.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Chemical Physics", journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse", received = "15 September 1953", } @Article{Royo:1954:TNA, author = "Jose Royo and Sebastian Ferrer", title = "Tabla de numeros aleatorios obtenida de los numeros de la {Loteria Nacional Espa{\~n}ola}. ({Spanish}) [{Tables} of random numbers obtained from numbers in the {Spanish National Lottery}]", journal = "Trabajos de Estad{\'\i}stica y de Investigaci{\'o}n Operativa", volume = "5", number = "2", pages = "247--256", month = "????", year = "1954", CODEN = "????", DOI = "https://doi.org/10.1007/BF03028546", ISSN = "0213-8190", bibdate = "Mon Jan 16 22:48:20 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Spanish", } @Article{Schwartz:1954:RPC, author = "Lorraine Schwartz", title = "Review of {P. C. Mahalanobis, {\em Tables of random samples from a normal population}}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "8", number = "??", pages = "228--??", month = "????", year = "1954", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Jun 27 15:46:11 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "108", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Taussky:1954:GTP, author = "Olga Taussky and John Todd", title = "Generation and Testing of Pseudo-Random Numbers", type = "Report", number = "3370", institution = pub-NBS, address = pub-NBS:adr, pages = "ii + 16", day = "22", month = jun, year = "1954", DOI = "https://doi.org/10.6028/nbs.rpt.3370", bibdate = "Thu Mar 29 10:01:35 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "https://nvlpubs.nist.gov/nistpubs/Legacy/RPT/nbsreport3370.pdf", abstract = "We shall confine our attention to generation and testing of sequences of pseudo-random numbers by arithmetical processes on automatic high speed digital computers. We shall also confine our attention mainly to a uniform distribution of random numbers not random digits. The approximation of normal deviates and other random variates by polynomials in uniform variates has been discussed in detail by Teichroew [13]; for other methods, e.g., acceptance or rejection methods, see von Neumann [6, 36--38] and Votaw and Rafferty [l6].", acknowledgement = ack-nhfb, author-dates = "Olga Taussky-Todd (30 August 1906--7 October 1995); John Todd (16 May 1911--21 June 2007)", } @Article{Tocher:1954:AAC, author = "K. D. Tocher", title = "The application of automatic computers to sampling experiments", journal = j-J-R-STAT-SOC-SER-B-METHODOL, volume = "16", number = "1", pages = "39--61", year = "1954", CODEN = "JSTBAJ", ISSN = "0035-9246", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Discussion pp. 61-75.", URL = "http://www.jstor.org/stable/2984009", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series B (Methodological)", HDnumber = "124", journal-URL = "http://www.jstor.org/journals/00359246.html", } @Article{Todd:1954:ESD, author = "John Todd", title = "Experiments in the solution of differential equations by {Monte Carlo} methods", journal = j-J-WASH-ACAD-SCI, volume = "44", number = "12", pages = "377--381", month = dec, year = "1954", CODEN = "JWASA3", ISSN = "0043-0439", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/24533326", acknowledgement = ack-nhfb, fjournal = "Journal of the Washington Academy of Sciences", HDnumber = "125", journal-URL = "http://www.jstor.org/journal/jwashacadscie", } @InProceedings{vanWijngaarden:1954:MC, author = "A. van Wijngaarden", title = "Mathematics and computing", crossref = "Anonymous:1954:ADC", pages = "125--129", year = "1954", bibdate = "Mon Jun 27 16:14:13 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "130", } @Article{vonSchelling:1954:CCU, author = "H. von Schelling", title = "Coupon collecting for unequal probabilities", journal = j-AMER-MATH-MONTHLY, volume = "61", number = "??", pages = "306--311", month = "????", year = "1954", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jan 16 22:49:37 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Book{Fieller:1955:CRN, author = "E. C. Fieller and T. Lewis and E. S. Pearson", title = "Correlated random normal deviates; 3,000 sets of deviates, each giving 9 random pairs with correlations $ 0.1 (0 \times 1) 0 \times 9 $", volume = "26", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "60", year = "1955", LCCN = "QA47 .T7 no.26", bibdate = "Mon Jun 27 13:35:14 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "Compiled from Herman Wold's Table of random normal deviates (Tract no. XXV) by E. C. Fieller, T. Lewis, and E. S. Pearson: {\em Random normal deviates}.", series = "Tracts for computers", acknowledgement = ack-nhfb, HDnumber = "27", subject = "Probabilities; Tables; Sampling (Statistics)", } @TechReport{Gilbert:1955:MCR, author = "E. N. Gilbert", title = "Machine Computation of random numbers", type = "Report", number = "MM-56-114-3", institution = "Bell Telephone Laboratories", address = "Murray Hill, NJ, USA", day = "12", month = mar, year = "1955", bibdate = "Mon Jun 27 14:22:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "34", } @TechReport{Golomb:1955:SRP, author = "S. W. Golomb", title = "Sequences with randomness properties", type = "Report", institution = "Glenn L. Martin Co.", address = "Baltimore, MD, USA", pages = "????", year = "1955", bibdate = "Thu Jan 19 06:49:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Greenwood:1955:CCT, author = "Robert E. Greenwood", title = "Coupon Collector's Test for Random Digits", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "9", number = "49", pages = "1--5", month = jan, year = "1955", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "43", journal-URL = "http://www.ams.org/mcom/", } @Book{Hastings:1955:ADC, author = "Cecil {Hastings, Jr.}", title = "Approximations for Digital Computers", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "viii + 201", year = "1955", ISBN = "0-691-07914-5", ISBN-13 = "978-0-691-07914-1", LCCN = "QA76 .H37", bibdate = "Mon Oct 01 15:59:48 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "Assisted by Jeanne T. Hayward and James P. Wong, Jr.", series = "The Rand series", acknowledgement = ack-nhfb, remark-1 = "Reprinted 1957, 1959, 1962, 1966, and 1970. I have fourth printing (1962).", remark-2 = "Hastings gives a polynomial approximation for computing random numbers from a normal distribution.", subject = "Electronic digital computers; Numerical analysis", tableofcontents = "Preface / v \\ Part I \\ 1: Concerning Best Fit / 3 \\ 2: Linear Weights / 19 \\ 3: An Iterative Procedure / 27 \\ 4: Solution of Equations / 35 \\ 5: Chebyshev Polynomials / 47 \\ 6: Concerning Weights / 65 \\ 7: Function With a Peak / 75 \\ 8: Rates of Convergence / 83 \\ 9: Choice of Form / 95 \\ 10: A Scoring-Camera Problem / 115 \\ Part II \\ 1: $\log_{10} x$ / 125 \\ 5: $\phi(x) = (1 - e^{-x}) / x$ / 129 \\ 8: $\arctan x$ / 132 \\ 14: $\sin (\pi/2) x$ / 138 \\ 17: $10^x$ / 141 \\ 21: $W(x) = e^{-x} / (1 + e^{-x})^2$ / 145 \\ 24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 \\ 27: $E'(x) = (1 / \sqrt{2 \pi}) e^{-(1/2)x^2}$ / 151 \\ 30: ``Total Klein-Nishina Cross Section'' Function / 154 \\ 31: $\Gamma(1 + x)$ / 155 \\ 35: $\arcsin x$ / 159 \\ 40: $\log_2 x$ / 164 \\ 43: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \, dt$ / 167 \\ 46: $K(k) = \int_0^{\pi/2} (1 / \sqrt{1 - k^2 \sin^2 \phi}) \, d\phi$ / 170 \\ 49: $E(k) = \int_0^{\pi/2} \sqrt{1 - k^2 \sin^2 \phi} \, d\phi$ / 173 \\ 52: $\ln(1 + x)$ / 176 \\ 57: $e^{-x}$ / 181 \\ 61: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \, dt$ / 185 \\ 64: $-{\rm Ei}(-x) = \int_x^\infty (e^{-t} / t) \, dt$ / 188 \\ 67: $q = (1 / \sqrt{2 \pi}) \int_{x(q)}^\infty e^{-(1/2)t^2} \, dt$ / 191 \\ 69: $W(z) = \int_0^\infty (e^(-u z) / (K_1^2(u) + \pi^2 I_1^2(u))) (1/u) \, du$ / 193 \\ 71: $P(x) = \int_x^\infty (\sin(t - x) / t) \, dt$ / 195 \\ 74: $Q(x) = \int_x^\infty (\cos(t - x) / t) \, dt$ / 195 \\ References for Part II / 201", } @Article{McCracken:1955:MCM, author = "Daniel D. McCracken", title = "The {Monte Carlo} Method", journal = j-SCI-AMER, volume = "192", number = "5", pages = "90--??", month = may, year = "1955", CODEN = "SCAMAC", ISSN = "0036-8733 (print), 1946-7087 (electronic)", ISSN-L = "0036-8733", bibdate = "Tue May 19 18:01:43 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Scientific American", journal-URL = "http://www.nature.com/scientificamerican", keywords = "Buffon needle problem; mathematics; Monte Carlo method; probability; random numbers", } @Article{Neovius:1955:ATT, author = "G{\"o}sta Neovius", title = "Artificial traffic trials using digital computers", journal = "Ericsson Technics", volume = "11", number = "??", pages = "279--291", year = "1955", CODEN = "????", ISSN = "0014-018X", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "90", } @Book{RAND:1955:MRD, author = "{RAND Corporation}", title = "A Million Random Digits With 100,000 Normal Deviates", publisher = pub-FREE, address = pub-FREE:adr, pages = "xxv + 400 + 200", year = "1955", ISBN = "0-02-925790-5", ISBN-13 = "978-0-02-925790-6", LCCN = "QA276.5 .R3", bibdate = "Sat Aug 23 07:58:03 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Reprinted in 1966 and 2001 \cite{RAND:2001:MRD}. See also \cite{Tippett:1927:RSN,Brown:1949:HRR,Brown:1951:HRR}.", URL = "http://www.rand.org/pubs/monograph_reports/MR1418.html", acknowledgement = ack-nhfb, HDnumber = "100", } @Article{Spenser:1955:RNT, author = "Gordon Spenser", title = "Random numbers and their generation", journal = j-COMP-AUTO, volume = "4", number = "??", pages = "10--11, 23", year = "1955", CODEN = "CPAUAJ", ISSN = "0010-4795, 0887-4549", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Computers and Automation", HDnumber = "114", } @Article{Barton:1956:SNO, author = "D. E. Barton and F. N. David", title = "Some notes on ordered random intervals", journal = j-J-R-STAT-SOC-SER-B-METHODOL, volume = "18", number = "1", pages = "79--94", month = "????", year = "1956", CODEN = "JSTBAJ", ISSN = "0035-9246", bibdate = "Sun Feb 19 06:48:10 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2983737", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series B (Methodological)", journal-URL = "http://www.jstor.org/journals/00359246.html", } @InProceedings{Butler:1956:MSG, author = "James W. Butler", title = "Machine sampling from given probability distributions", crossref = "Meyer:1956:SMC", pages = "249--264", year = "1956", bibdate = "Mon Jun 27 12:23:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "12", } @Article{Davis:1956:SMC, author = "P. Davis and P. Rabinowitz", title = "Some {Monte Carlo} Experiments in Computing Multiple Integrals", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "10", number = "53", pages = "1--8", month = jan, year = "1956", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "21", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Farrington:1956:GPR, author = "Carl C. {Farrington, Jr.}", title = "Generating pseudo-random numbers in the {Illiac}", type = "Report", number = "74", institution = "Digital Computer Laboratory, University of Illinois", address = "Champaign-Urbana, IL, USA", year = "1956", bibdate = "Mon Jun 27 13:33:15 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "26", } @Article{Isida:1956:RNG, author = "Masatugu Isida and Hiroji Ikeda", title = "Random number generator", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "8", number = "??", pages = "119--126", year = "1956", CODEN = "AISXAD", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", MRnumber = "MR 86369", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Annals of the Institute of Statistical Mathematics (Tokyo)", HDnumber = "4'", journal-URL = "http://link.springer.com/journal/10463", } @Article{Johnson:1956:GTP, author = "D. L. Johnson", title = "Generating and Testing Pseudo Random Numbers on the {IBM Type 701}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "10", number = "53", pages = "8--13", month = jan, year = "1956", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "57", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Kahn:1956:AMC, author = "Herman Kahn", title = "Applications of {Monte Carlo}", type = "Research Memorandum", number = "RM-1237", institution = "RAND Corporation", address = "Santa Monica, CA, USA", year = "1956", bibdate = "Mon Jun 27 14:58:22 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Also appeared as AECU 3259", URL = "http://www.rand.org/pubs/research_memoranda/RM1237.html", abstract = "A discussion of some of the ideas and techniques of the Monte Carlo method (applying probability theory and statistics to applied mathematics) that have proved useful in the solution of various problems. The study considers techniques with random variables, evaluating integrals, integral or matrix equations, and ordinary differential equations.", acknowledgement = ack-nhfb, HDnumber = "59", } @InProceedings{Kahn:1956:UDM, author = "Herman Kahn", title = "Use of different {Monte Carlo} sampling techniques", crossref = "Meyer:1956:SMC", pages = "146--190", year = "1956", bibdate = "Mon Jun 27 14:59:48 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "60", } @InProceedings{Lytle:1956:DGT, author = "Ernest J. {Lytle, Jr.}", title = "A description of the generation and testing of a set of random normal deviates", crossref = "Meyer:1956:SMC", pages = "234--248", year = "1956", bibdate = "Mon Jun 27 14:59:48 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "72", } @InProceedings{Marshall:1956:UMS, author = "Andrew W. Marshall", title = "The use of multi-stage sampling schemes in {Monte Carlo} computations", crossref = "Meyer:1956:SMC", pages = "123--140", year = "1956", bibdate = "Mon Jun 27 15:19:05 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "79", } @InProceedings{Metropolis:1956:DGT, author = "N. Metropolis", title = "A description of the generation and testing of a set of random normal deviates", crossref = "Meyer:1956:SMC", pages = "234--248", year = "1956", bibdate = "Mon Jun 27 14:59:48 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @InProceedings{Metropolis:1956:PSM, author = "N. Metropolis", title = "Phase shifts --- middle squares --- wave equations", crossref = "Meyer:1956:SMC", pages = "29--36", year = "1956", MRclass = "65.3X", MRnumber = "MR0088787 (19,580c)", MRreviewer = "M. A. Hyman", bibdate = "Thu Dec 22 07:41:05 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Lecture notes in statistics", acknowledgement = ack-nhfb, HDnumber = "82", } @Article{Pawlak:1956:FFG, author = "Z. Pawlak", title = "Flip-flop as generator of random binary digits", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "10", number = "??", pages = "28--30", year = "1956", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Jun 27 15:35:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "96", journal-URL = "http://www.ams.org/mcom/", } @Article{Sprowls:1956:ACF, author = "R. Clay Sprowls", title = "An Automatic Coin Flipper for Sampling Demonstrations", journal = j-AMER-STAT, volume = "10", number = "2", pages = "12--13", month = apr, year = "1956", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 08:42:51 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326299; https://www.math.utah.edu/pub/tex/bib/amstat1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2681598", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Stuart:1956:ETR, author = "Alan Stuart", title = "The efficiencies of tests of randomness, distribution-free methods vs. normal alternatives", journal = j-J-AM-STAT-ASSOC, volume = "51", number = "274", pages = "285--287", month = jun, year = "1956", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Jan 16 22:46:41 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281348", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @InProceedings{Taussky:1956:GTP, author = "Olga Taussky and John Todd", title = "Generation and testing of pseudo-random numbers", crossref = "Meyer:1956:SMC", pages = "15--28", year = "1956", MRnumber = "MR 80382", bibdate = "Mon Jun 27 12:23:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "118", } @InProceedings{Tompkins:1956:MAP, author = "C. B. Tompkins", title = "Machine attacks on problems whose variables are permutations", crossref = "Curtiss:1956:NAP", pages = "195--212", year = "1956", bibdate = "Mon Jun 27 16:11:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "129", } @Article{Tompkins:1956:RJS, author = "C. B. Tompkins", title = "Review of {{\em Japanese Standards Association, random number generating icosahedral dice}}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "15", number = "73", pages = "94--95", month = jan, year = "1956", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "127", journal-URL = "http://www.ams.org/mcom/", } @Article{Tompkins:1956:RMR, author = "C. B. Tompkins", title = "Review of {{\em A Million Random Digits With 100,000 Normal Deviates}}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "10", number = "53", pages = "39--43", month = jan, year = "1956", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "127", journal-URL = "http://www.ams.org/mcom/", } @Article{Cook:1957:RFP, author = "J. M. Cook", title = "Rational Formulae for the Production of a Spherically Symmetric Probability Distribution", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "11", number = "58", pages = "81--82", month = apr, year = "1957", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Feb 27 08:05:17 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/2002156", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", journal-URL = "http://www.ams.org/mcom/", remark = "Extension to the surface of a sphere of von Neumann's method for producing a uniform distribution of random value on the circumference of the unit circle.", } @Article{Davis:1957:CJH, author = "Harold Davis", title = "Comment: {J. Halcomb Laning, Jr., and Richard H. Battin, \booktitle{Random Processes in Automatic Control}, McGraw-Hill Series in Control Systems Engineering, McGraw-Hill Book Co., Inc., New York, 1956, ix + 434 p., 23 cm. Price \$10.00}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "11", number = "58", pages = "112--112", month = apr, year = "1957", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Mon Feb 27 08:05:17 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/2002157", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", journal-URL = "http://www.ams.org/mcom/", } @Book{Fisher:1957:STBa, author = "Sir Ronald Aylmer Fisher and Frank Yates", title = "Statistical tables for biological, agricultural, and medical research", publisher = pub-OLIVER-BOYD, address = pub-OLIVER-BOYD:adr, edition = "Fifth", pages = "138", year = "1957", LCCN = "QA276 .F498 1957a", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (1890--1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc; Mathematical statistics", } @Book{Fisher:1957:STBb, author = "Sir Ronald Aylmer Fisher and Frank Yates", title = "Statistical tables for biological, agricultural, and medical research", publisher = "Hafner Pub. Co.", address = "New York, NY, USA", edition = "Fifth", pages = "138", year = "1957", LCCN = "QA276 .F498 1957", bibdate = "Thu Dec 22 09:30:04 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (1890--1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc; Mathematical statistics", } @Article{Gabai:1957:DCS, author = "H. Gabai", title = "On the discrepancy of certain sequences mod $1$", journal = "Ill. J. Math.", volume = "1", pages = "1--12", year = "1957", bibdate = "Wed Mar 28 06:06:24 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0146.06303", acknowledgement = ack-nhfb, keywords = "number theory", language = "English", } @Article{Good:1957:STR, author = "I. J. Good", title = "On the serial test for random sequences", journal = j-ANN-MATH-STAT, volume = "28", number = "1", pages = "262--264", month = mar, year = "1957", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177707053", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177707053; http://www.jstor.org/stable/2237039", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "39", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Savage:1957:ITR, author = "Richard Savage", title = "On the Independence of Tests of Randomness and Other Hypotheses", journal = j-J-AM-STAT-ASSOC, volume = "52", number = "277", pages = "53--57", month = mar, year = "1957", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:32 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314156; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281400", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{vonHoerner:1957:HZR, author = "Sebastian von Hoerner", title = "{Herstellung von Zufallszahlen auf Rechenautomaten}. ({German}) [{Production} of random numbers on automatic computers]", journal = j-Z-ANGE-MATH-PHYS, volume = "8", number = "??", pages = "26--52", year = "1957", CODEN = "ZAMPDB", ISSN = "0044-2275 (print), 1420-9039 (electronic)", ISSN-L = "0044-2275", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics}", HDnumber = "132", journal-URL = "http://link.springer.com/journal/33", language = "German", } @Article{Walsh:1957:EMO, author = "John E. Walsh", title = "An experimental method for obtaining random digits and permutations", journal = j-SANKHYA-A, volume = "17", number = "5", pages = "355--360", month = feb, year = "1957", CODEN = "SNKYA5", ISSN = "0036-4452", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/25048325", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", HDnumber = "138", } @Article{Bass:1958:MMC, author = "J. Bass and J. Guilloud", title = "{M{\'e}thode} de {Monte-Carlo} et suites uniform{\'e}ment denses. ({French}) [{The Monte Carlo Method} and sequences of uniformly-distributed numbers]", journal = j-CHIFFRES, volume = "1", number = "??", pages = "149--156", month = "????", year = "1958", CODEN = "????", ISSN = "0245-9922", bibdate = "Mon Jun 27 12:08:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Chiffres: Revue de l'Association fran{\c{c}}aise de Calcul", HDnumber = "2", language = "French", } @Article{Bauer:1958:MCM, author = "W. F. Bauer", title = "The {Monte Carlo} Method", journal = j-J-SIAM, volume = "6", number = "4", pages = "438--451", month = dec, year = "1958", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics", HDnumber = "4", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Book{Bendat:1958:PAR, author = "Julius S. Bendat", title = "Principles and Applications of Random Noise Theory", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "431", year = "1958", LCCN = "TK5101 .B37", bibdate = "Sun Nov 30 07:47:29 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Random noise theory", } @Article{Bofinger:1958:PPP, author = "Eve Bofinger and V. J. Bofinger", title = "On a Periodic Property of Pseudo-Random Sequences", journal = j-J-ACM, volume = "5", number = "3", pages = "261--265", month = jul, year = "1958", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/320932.320937", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:06:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", HDnumber = "5", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Box:1958:NGR, author = "G. E. P. Box and Mervin E. Muller", title = "A note on the generation of random normal deviates", journal = j-ANN-MATH-STAT, volume = "29", number = "2", pages = "610--611", month = jun, year = "1958", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177706645", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Sat Sep 17 10:06:44 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177706645; http://www.jstor.org/stable/2237361", abstract = "Sampling experiments often require the generation of large numbers of random normal deviates. When an electronic computer is used it is desirable to arrange for the generation of such normal deviates within the machine itself rather than to rely on tables. Pseudo random numbers can be generated by a variety of methods within the machine and the purpose of this note is to give what is believed to be a new method for generating normal deviates from independent random numbers. This approach can be used on small as well as large scale computers. A detailed comparison of the utility of this approach with other known methods (such as: (1) the inverse Gaussian function of the uniform deviates, (2) Teichroew's approach, (3) a rational approximation such as that developed by Hastings, (4) the sum of a fixed number of uniform deviates and (5) rejection-type approach), has been made elsewhere [1] by one of the authors (M. E. M.). It is shown that the present approach not only gives higher accuracy than previous methods but also compares in speed very favourably with other methods.", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "8", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Certaine:1958:SPR, author = "J. Certaine", title = "On Sequences of Pseudo-Random Numbers of Maximal Length", journal = j-J-ACM, volume = "5", number = "4", pages = "353--356", month = oct, year = "1958", CODEN = "JACOAH", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:10:19 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", HDnumber = "16", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Franklin:1958:EPR, author = "J. N. Franklin", title = "On the equidistribution of pseudo-random numbers", journal = j-QUART-APPL-MATH, volume = "16", number = "??", pages = "183--188", month = "????", year = "1958", CODEN = "QAMAAY", ISSN = "0033-569x (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Quarterly of Applied Mathematics", HDnumber = "31", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", } @TechReport{Gross:1958:AGP, author = "O. Gross and S. M. Johnson", title = "Additive generation of pseudorandom numbers", type = "Research Memorandum", number = "RM-2132", institution = "RAND Corporation", address = "Santa Monica, CA, USA", year = "1958", bibdate = "Mon Jun 27 14:33:22 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.rand.org/pubs/research_memoranda/RM2132.html", abstract = "The calculation of the cycle lengths of sequences of certain special cases of pseudorandom vectors generated by a new addition technique. These cycle lengths are comparable to those obtained by the established multiplicative methods, and relevant theorems are included. A pseudorandom sequence of numbers is defined as a completely determined sequence having some of the more easily tested statistical properties of truly random sequences.", acknowledgement = ack-nhfb, HDnumber = "44", } @Article{Leslie:1958:PSM, author = "P. H. Leslie and J. C. Gower", title = "The Properties of a Stochastic Model for two Competing Species", journal = j-BIOMETRIKA, volume = "45", number = "3/4", pages = "316--330", month = dec, year = "1958", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2333181", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", MRclass = "92.00 (60.00)", MRnumber = "0102448 (21 \#1241)", MRreviewer = "M. A. Stone", bibdate = "Sat Jun 21 14:32:58 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315431; https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2333181", acknowledgement = ack-nhfb, fjournal = "Biometrika", HDnumber = "69", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", } @Article{Muller:1958:IMG, author = "Mervin E. Muller", title = "An Inverse Method for the Generation of Random Normal Deviates on Large-Scale Computers", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "12", number = "63", pages = "167--174", month = jul, year = "1958", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematical Tables and Other Aids to Computation", HDnumber = "86", journal-URL = "http://www.ams.org/mcom/", } @Article{Renyi:1958:ODP, author = "Alfr{\'e}d R{\'e}nyi", title = "On a one-dimensional problem concerning random space filling", journal = "Magyar Tud. Akad. Mat. Kutat{\'o} Int. K{\"o}zl.", volume = "3", number = "1--2", pages = "109--127", month = "????", year = "1958", bibdate = "Wed Feb 29 21:10:40 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/kepler.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Publ. Math. Inst. Hung. Acad. Sci.", fjournal = "A Magyar Tudom{\'a}nyos Akad{\'e}mia Matematikai {\'e}s Fizikai Tudom{\'a}nyok Oszt{\'a}ly{\'a}nak K{\"o}zlem{\'e}nyei", keywords = "parking-lot test; sphere packing", language = "Hungarian (with English and Russian summaries)", } @TechReport{Richtmyer:1958:NRS, author = "R. D. Richtmyer", title = "A non-random sampling method, based on congruences, for {``Monte Carlo''} problems", type = "Report", number = "NYO-8674", institution = "AEC Computational and Applied Mathematics Center, New York University", address = "New York, NY, USA", year = "1958", bibdate = "Mon Jun 27 15:40:58 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "103", } @Article{Schmid:1958:KSL, author = "Paul Schmid", title = "On the {Kolmogorov} and {Smirnov} limit theorems for discontinuous distribution functions", journal = j-ANN-MATH-STAT, volume = "29", number = "4", pages = "1011--1027", month = dec, year = "1958", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Wed Jan 18 08:24:23 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2236943", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Sengupta:1958:TRN, author = "J. M. Sengupta and Nikhilesh Bhattacharya", title = "Tables of random normal deviates", journal = j-SANKHYA-A, volume = "20", number = "3/4", pages = "249--286", month = dec, year = "1958", CODEN = "SNKYA5", ISSN = "0036-4452", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", HDnumber = "109", } @Article{Sobol:1958:PRN, author = "I. M. Sobol'", title = "Pseudo-random numbers for the machine {``Strela''}", journal = j-THEORY-PROBAB-APPL, volume = "3", number = "2", pages = "192--197", month = "????", year = "1958", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/1103019", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/3/2; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", HDnumber = "111", journal-URL = "http://epubs.siam.org/tvp", onlinedate = "January 1958", } @Article{Thomson:1958:MCM, author = "W. E. Thomson", title = "A modified congruence method of generating pseudo-random numbers", journal = j-COMP-J, volume = "1", number = "2", pages = "83, 86", month = jul, year = "1958", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:55:03 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/010083.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/83.tif", acknowledgement = ack-nhfb, fjournal = "The Computer Journal", HDnumber = "120", journal-URL = "http://comjnl.oxfordjournals.org/", } @Article{Bolshev:1959:TRV, author = "L. N. Bol'shev", title = "On transformations of random variables", journal = j-THEORY-PROBAB-APPL, volume = "4", number = "2", pages = "136--149", month = "????", year = "1959", CODEN = "TPRBAU", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Wed Jan 18 11:09:54 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", } @Book{Cashwell:1959:PMM, author = "E. D. Cashwell and C. J. (Cornelius Joseph) Everett", title = "A practical manual on the {Monte Carlo} method for random walk problems", volume = "1", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "ix + 153", year = "1959", LCCN = "QC174.5 .C3", bibdate = "Mon Jun 27 12:30:13 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "International tracts in computer science and technology and their application", acknowledgement = ack-nhfb, HDnumber = "15", subject = "Quantum statistics; Probabilities; Computers", tableofcontents = "1. Basic principles (pseudo-random numbers) \\ 2. The source routine \\ 3. The mean free path and transmission \\ 4. The collision or escape routine \\ 5. The collision routine for neutrons \\ 6. Photon collisions \\ 7. Direction parameters aft~r collision \\ 8. Terminal classification \\ 9. Remarks on computation \\ 10. Statistical considerations \\ Appendix: Summary of problems run on Maniac I", } @Article{Cook:1959:RRP, author = "J. M. Cook", title = "Remarks on a Recent Paper: {``An Efficient Method for Generating Uniformly Distributed Points on the Surface of an $n$-Dimensional Sphere'' ({\bf 2}, No. 4 (1959), 17)}", journal = j-CACM, volume = "2", number = "10", pages = "26--26", month = oct, year = "1959", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/368453.1127876", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Mar 17 12:26:12 2012", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Cook59; https://www.math.utah.edu/pub/tex/bib/cacm1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Hicks:1959:EMG}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", oldlabel = "Cook59", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Cook59", } @Article{Ehrlich:1959:MCS, author = "Louis W. Ehrlich", title = "{Monte Carlo} Solutions of Boundary Value Problems Involving the Difference Analogue of $ \partial^2 u / \partial x^2 + \partial^2 u / \partial y^2 + ({K} / y)(\partial u / \partial y) = 0 $", journal = j-J-ACM, volume = "6", number = "2", pages = "204--218", month = apr, year = "1959", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/320964.320977", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:04:29 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", HDnumber = "25", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Golenko:1959:DCS, author = "D. I. Golenko", title = "Determination of characteristics of some stochastic processes by {Monte Carlo} methods", journal = j-COMP-MATH, volume = "??", number = "5", pages = "93--108", year = "1959", CODEN = "????", ISSN = "????", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Computational Mathematics", HDnumber = "36", language = "Russian", } @Article{Golenko:1959:FRN, author = "D. I. Golenko", title = "Formation of random numbers with arbitrary law of distribution", journal = j-COMP-MATH, volume = "??", number = "5", pages = "83--92", year = "1959", CODEN = "????", ISSN = "????", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Computational Mathematics", HDnumber = "35", language = "Russian", } @Article{Green:1959:ETA, author = "Bert F. {Green, Jr.} and J. E. Keith Smith and Laura Klem", title = "Empirical Tests of an Additive Random Number Generator", journal = j-J-ACM, volume = "6", number = "4", pages = "527--537", month = oct, year = "1959", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/320998.321006", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:10:59 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", HDnumber = "40", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Hicks:1959:EMG, author = "J. S. Hicks and R. F. Wheeling", title = "An Efficient Method for Generating Uniformly Distributed Points on the Surface of an $n$-Dimensional Sphere", journal = j-CACM, volume = "2", number = "4", pages = "17--19", month = apr, year = "1959", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/377939.377945", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Wed Jul 14 15:48:22 MDT 2004", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#HicksW59; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/cacm1950.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See remarks \cite{Cook:1959:RRP}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", oldlabel = "HicksW59", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HicksW59", } @Manual{IBM:1959:RNG, author = "{IBM}", title = "Random number generation and testing", organization = "International Business Machines Corporation", address = "New York, NY, USA", year = "1959", bibdate = "Mon Jun 27 14:55:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Reference manual C20-8011.", acknowledgement = ack-nhfb, HDnumber = "56", } @InProceedings{Lehmer:1959:CPD, author = "D. H. Lehmer", title = "Combinatorial problems with digital computers", crossref = "Macphail:1959:PFC", pages = "160--173", year = "1959", bibdate = "Mon Jun 27 15:08:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "68", } @Article{Muller:1959:CMG, author = "Mervin E. Muller", title = "A Comparison of Methods for Generating Normal Deviates on Digital Computers", journal = j-J-ACM, volume = "6", number = "3", pages = "376--383", month = jul, year = "1959", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/320986.320992", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Tue Nov 1 09:33:26 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, descriptors = "RVG", fjournal = "Journal of the Association for Computing Machinery", HDnumber = "87", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Muller:1959:NMG, author = "Mervin E. Muller", title = "A Note on a Method for Generating Points Uniformly on {$N$}-Dimensional Spheres", journal = j-CACM, volume = "2", number = "4", pages = "19--20", month = apr, year = "1959", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Wed Jul 14 15:48:22 MDT 2004", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Muller59; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", HDnumber = "88", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", oldlabel = "Muller59", remark = "See also \cite{Cheng:1998:RVG} for random points on an $n$-sphere.", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Muller59", } @Article{Page:1959:PRE, author = "E. S. Page", title = "Pseudo-Random Elements for Computers", journal = j-APPL-STAT, volume = "8", number = "2", pages = "124--131", month = jun, year = "1959", CODEN = "APSTAG", ISSN = "0035-9254 (print), 1467-9876 (electronic)", ISSN-L = "0035-9254", bibdate = "Sat Apr 21 10:16:50 MDT 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Applied Statistics", HDnumber = "94", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues", } @Article{Schulz-Arenstorff:1959:PDP, author = "Richard Schulz-Arenstorff and James C. Morelock", title = "The Probability Distribution of the Product of $n$ Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "66", number = "2", pages = "95--99", month = feb, year = "1959", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:39:17 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Sterzer:1959:RNG, author = "Fred Sterzer", title = "Random number generator using subharmonic oscillators", journal = j-REV-SCI-INSTRUM, volume = "30", number = "4", pages = "241--243", year = "1959", CODEN = "RSINAK", DOI = "https://doi.org/10.1063/1.1716525", ISSN = "1089-7623, 0034-6748", ISSN-L = "0034-6748", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A random number generator which uses two 2000 Mc subharmonic oscillators is described. This generator can produce random binary digits at a maximum rate of approximately $ 3 \times 10^7 $ digits per second. Statistical tests performed on over a quarter million digits produced by this generator indicate that they were at least as random as digits produced by other slower contemporary means.", acknowledgement = ack-nhfb, fjournal = "Review of scientific instruments", HDnumber = "115", journal-URL = "http://rsi.aip.org/", } @Article{Thomson:1959:EMS, author = "W. E. Thomson", title = "{ERNIE} --- a mathematical and statistical analysis", journal = j-J-R-STAT-SOC-SER-A-GENERAL, volume = "122", number = "3", pages = "301--324", year = "1959", CODEN = "JSSAEF", ISSN = "0035-9238", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Discussion pp. 324-333.", URL = "http://www.jstor.org/stable/2342795", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series A (General)", HDnumber = "121", journal-URL = "http://www.jstor.org/journals/00359238.html", keywords = "ERNIE (Electronic Random Number Generator Indicator Equipment)", xxpages = "301--333", } @Book{Tippett:1959:RSN, author = "Leonard Henry Caleb Tippett", title = "Random sampling numbers", volume = "15", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "viii + 26", year = "1959", LCCN = "QA47 .T7 no. 15", bibdate = "Mon Jun 27 13:35:14 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "With a foreword by editor Karl Pearson.", series = "Tracts for computers", acknowledgement = ack-nhfb, HDnumber = "123", remark = "This is a reprint of \cite{Tippett:1927:RSN}.", subject = "Mathematics; Tables; Sampling (Statistics)", } @Article{Zierler:1959:LRS, author = "Neal Zierler", title = "Linear Recurring Sequences", journal = j-J-SIAM, volume = "7", number = "1", pages = "31--48", month = mar, year = "1959", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics", HDnumber = "143", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Article{Bazley:1960:AMC, author = "N. W. Bazley and P. J. Davis", title = "Accuracy of {Monte Carlo} methods in computing finite {Markov} chains", journal = j-J-RES-NATL-BUR-STAND-1934, volume = "64B", number = "??", pages = "211--215", month = "????", year = "1960", CODEN = "????", ISSN = "0091-0635", bibdate = "Mon Jun 27 12:11:11 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Research of the National Bureau of Standards (1934)", HDnumber = "3", } @InProceedings{Butcher:1960:SR, author = "J. C. Butcher", editor = "????", booktitle = "Proceedings of the First Australian Computer Conference", title = "The simulation of randomness", publisher = "????", address = "????", pages = "12/1/1--12/1/2", year = "1960", LCCN = "????", bibdate = "Mon Jan 16 22:40:20 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "????", acknowledgement = ack-nhfb, } @Book{Clark:1960:EDR, author = "Charles E. (Charles Erwin) Clark and Betty Weber Holz", title = "Exponentially distributed random numbers", publisher = "Published for Operations Research Office, Johns Hopkins University by Johns Hopkins Press", address = "Baltimore, MD, USA", pages = "249", year = "1960", LCCN = "QA276 .C49", bibdate = "Mon Jun 27 12:32:41 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, HDnumber = "18", subject = "Numbers, Random", } @Article{Clark:1960:USR, author = "Charles E. Clark", title = "The utility of statistics of random numbers", journal = j-OPER-RES, volume = "8", number = "2", pages = "185--195", month = mar # "\slash " # apr, year = "1960", CODEN = "OPREAI", DOI = "https://doi.org/10.1287/opre.8.2.185", ISSN = "0030-364X (print), 1526-5463 (electronic)", ISSN-L = "0030-364X", bibdate = "Mon Jun 27 12:17:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/167201", acknowledgement = ack-nhfb, fjournal = "Operations Research", HDnumber = "17", journal-URL = "http://pubsonline.informs.org/loi/opre", } @Article{Coveyou:1960:SCG, author = "R. R. Coveyou", title = "Serial Correlation in the Generation of Pseudo-Random Numbers", journal = j-J-ACM, volume = "7", number = "1", pages = "72--74", month = jan, year = "1960", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321008.321018", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:01:31 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", HDnumber = "19", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @TechReport{DeMatteis:1960:PRS, author = "A. {De Matteis} and B. Faleschini", title = "Pseudo-random sequences of equal length", type = "Report", number = "88", institution = "Comitato AND Nazionale per l'Energia Nucleare", address = "Bologna, Italy", year = "1960", bibdate = "Mon Jun 27 15:20:20 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "80", } @Article{Edmonds:1960:GPR, author = "A. R. Edmonds", title = "The generation of pseudo-random numbers on electronic digital computers", journal = j-COMP-J, volume = "2", number = "4", pages = "181--185", month = jan, year = "1960", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:55:16 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/020181.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/tiff/181.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/tiff/182.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/tiff/183.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/tiff/184.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_04/tiff/185.tif", acknowledgement = ack-nhfb, fjournal = "The Computer Journal", HDnumber = "24", journal-URL = "http://comjnl.oxfordjournals.org/", } @Article{Golenko:1960:SRN, author = "D. I. Golenko and V. P. Smiriagin", title = "A source of random numbers which are equidistributed in $ [0, 1] $", journal = "Publications Math. Inst., Hungarian Acad. Sci.", volume = "5A", number = "3", pages = "241--253", year = "1960", CODEN = "????", ISSN = "????", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "English abstract.", acknowledgement = ack-nhfb, HDnumber = "37", language = "Russian", } @InCollection{Good:1960:MCM, author = "I. J. Good", booktitle = "{McGraw-Hill} Encyclopedia of Science and Technology", title = "{Monte Carlo} Method", volume = "8", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "586--587", year = "1960", LCCN = "????", bibdate = "Sat Jan 07 11:52:13 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Halton:1960:BEC, author = "J. H. Halton", title = "{Berichtigung: ``On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals'' [Num. Math. {\bf 2}, 84--90 (1960)]}. ({German}) [{Correction}]", journal = j-NUM-MATH, volume = "2", pages = "196--196", month = dec, year = "1960", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon Oct 18 21:30:25 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Halton:1960:ECQ}.", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", language = "German, English", } @Article{Halton:1960:ECQ, author = "J. H. Halton", title = "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals", journal = j-NUM-MATH, volume = "2", pages = "84--90", month = dec, year = "1960", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Sun Oct 17 19:01:15 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See correction \cite{Halton:1960:BEC}.", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", HDnumber = "47", journal-URL = "http://link.springer.com/journal/211", } @Article{Hammersley:1960:MCM, author = "J. M. Hammersley", title = "{Monte Carlo} methods for solving multivariable problems", journal = j-ANN-NY-ACAD-SCI, volume = "86", number = "??", pages = "844--874", year = "1960", CODEN = "ANYAA9", ISSN = "0077-8923 (print), 1749-6632 (electronic)", ISSN-L = "0077-8923", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Annals of the New York Academy of Sciences", HDnumber = "50", journal-URL = "http://www.nyas.org/Publications/Archive.aspx", } @Article{Hunter:1960:NTR, author = "D. G. N. Hunter", title = "Note on a test for repeating cycles in a pseudo-random number generator", journal = j-COMP-J, volume = "3", number = "1", pages = "9--9", month = apr, year = "1960", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:55:18 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/030009.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/9.tif", acknowledgement = ack-nhfb, fjournal = "The Computer Journal", HDnumber = "55", journal-URL = "http://comjnl.oxfordjournals.org/", } @TechReport{Kleinrock:1960:PTS, author = "L. Kleinrock", title = "A Program for Testing Sequences of Random Numbers", type = "Report", number = "51G-0018", institution = "MIT Lincoln Laboratory", address = "Cambridge, MA, USA", day = "25", month = oct, year = "1960", bibdate = "Thu Feb 02 17:32:52 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1960:GED, author = "George Marsaglia", title = "On generating exponentially distributed random variables", type = "Report", number = "??", institution = "Boeing Scientific Research Labs", address = "Seattle, WA, USA", pages = "??", month = "????", year = "1960", bibdate = "Tue Jun 21 18:58:31 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Pakov:1960:GRC, author = "G. K. Pakov", title = "Generation of a random correlated quantity on a high-speed electronic computer", journal = "Soviet developments in information processing and machine translation", volume = "??", number = "??", pages = "??--??", month = "????", year = "1960", CODEN = "????", ISSN = "????", bibdate = "Mon Jun 27 15:33:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "U. S. Joint Publ. Res. Service JPRS: 5784, Nov., 1960", acknowledgement = ack-nhfb, ajournal = "Soviet Develop. Infor. Proc. Machine Translat.", HDnumber = "95", keywords = "true random numbers from physical sources", } @Article{Postnikov:1960:AMR, author = "A. G. Postnikov", title = "Arithmetic modeling of random processes", journal = j-PROC-STEKLOV-INST-MATH, volume = "57", number = "??", pages = "1--84", month = "????", year = "1960", CODEN = "TMISAF", ISSN = "0371-9685", MRclass = "10.50", MRnumber = "0148639 (26 \#6146)", MRreviewer = "A. R{\'e}nyi", bibdate = "Thu Jan 19 08:10:22 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Trudy Matematicheskogo instituta imeni V. A. Steklova = Proceedings of the Steklov Institute of Mathematics", } @Article{Rotenburg:1960:NPR, author = "A. Rotenburg", title = "A New Pseudo-Random Number Generator", journal = j-J-ACM, volume = "7", number = "1", pages = "75--77", month = jan, year = "1960", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321008.321019", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:01:32 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, descriptors = "RNG; linear congruential generator", fjournal = "Journal of the Association for Computing Machinery", HDnumber = "107", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Schmidt:1960:NN, author = "Wolfgang M. Schmidt", title = "On normal numbers", journal = j-PAC-J-MATH, volume = "10", pages = "661--672", year = "1960", CODEN = "PJMAAI", ISSN = "0030-8730 (print), 1945-5844 (electronic)", ISSN-L = "0030-8730", MRclass = "10.00", MRnumber = "0117212 (22 \#7994)", MRreviewer = "F. Herzog", bibdate = "Sat Jan 7 16:44:42 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/pi.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.pjm/1103038420", ZMnumber = "0093.05401", acknowledgement = ack-nhfb, fjournal = "Pacific Journal of Mathematics", journal-URL = "http://msp.org/pjm", remark = "From the first section of the paper: ``In this paper we solve the following problem. {\em Under what conditions on $r$, $s$ is every number $ \xi $ which is normal to base $r$ also normal to base $s$ ?} The answer is given by: THEOREM 1. {\bf A} Assume $ r \sim s $. Then any number normal to base $r$ is normal to base $s$. {\bf B} If $ r \not \sim s $, then the set of numbers $ \xi $ which are normal to base $r$ but not even simply normal to base $s$ has the power of the continuum.'' Here, the relation $ r \sim s $ means that the exist integer $m$ and $n$ such that $ r^m = s^n $.", } @Article{Wall:1960:FSM, author = "D. D. Wall", title = "{Fibonacci} Series Modulo $m$", journal = j-AMER-MATH-MONTHLY, volume = "67", number = "6", pages = "525--532", month = jun # "\slash " # jul, year = "1960", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:35:58 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", HDnumber = "135", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @InProceedings{Wall:1960:RNT, author = "Donald D. Wall", title = "A random number test for large samples", crossref = "Anonymous:1960:PFI", pages = "7--11", year = "1960", bibdate = "Mon Jun 27 16:20:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "136", } @Article{Yamada:1960:PPN, author = "S. Yamada", title = "On the period of pseudorandom numbers generated by {Lehmer}'s congruential method", journal = "J. Op. Research Soc. Japan", volume = "3", number = "??", pages = "113--123", month = "????", year = "1960", CODEN = "????", ISSN = "????", bibdate = "Mon Jan 16 22:43:38 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Book{Biuslenko:1961:MCM, author = "N. P. Biuslenko and Ju. A. Sreider", title = "The {Monte-Carlo} method and how it is carried out on digital computers", publisher = "Gosudarstv. Izdat. Fiz-Mat. Lit.", address = "Moscow, USSR", pages = "????", year = "1961", CODEN = "????", ISSN = "????", LCCN = "????", bibdate = "Mon Jun 27 16:32:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "1'", language = "Russian", } @Article{Bofinger:1961:GTR, author = "Eve Bofinger and V. J. Bofinger", title = "The gap test for random sequences", journal = j-ANN-MATH-STAT, volume = "32", number = "2", pages = "524--534", month = jun, year = "1961", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177705058", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jun 27 12:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177705058; http://www.jstor.org/stable/2237761", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "6", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Bofinger:1961:NPW, author = "Eve Bofinger and V. J. Bofinger", title = "A note on the paper by {W. E. Thomson, on {\em ERNIE --- a mathematical and statistical analysis}}", journal = j-J-R-STAT-SOC, volume = "A124", number = "??", pages = "240--243", month = "????", year = "1961", CODEN = "????", ISSN = "0952-8385", bibdate = "Mon Jun 27 12:14:09 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "J. Roy. Stat. Soc.", fjournal = "Journal of the Royal Statistical Society", HDnumber = "7", journal-URL = "http://www.jstor.org/journals/09528385.html", keywords = "ERNIE (Electronic Random Number Generator Indicator Equipment)", } @Article{Bofinger:1961:RTS, author = "Eve Bofinger and V. J. Bofinger", title = "A Runs Test for Sequences of Random Digits", journal = j-AUST-J-STAT, volume = "3", number = "2", pages = "37--41", month = aug, year = "1961", CODEN = "AUJSA3", DOI = "https://doi.org/10.1111/j.1467-842X.1961.tb00307.x", ISSN = "0004-9581", ISSN-L = "0004-9581", bibdate = "Fri Jul 15 14:27:36 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/anzjs.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Australian Journal of Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues", } @Article{Brandt:1961:GCT, author = "A. Brandt", title = "A generalization of a combinatorial theorem of {Sparre Andersen} about sums of random variables", journal = j-MATH-SCAND, volume = "9", pages = "325--358", year = "1961", CODEN = "MTSCAN", ISSN = "0025-5521 (print), 1903-1807 (electronic)", ISSN-L = "0025-5521", bibdate = "Fri Jan 6 09:58:10 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/brandt-achi.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematica Scandinavica", journal-URL = "http://www.mscand.dk/issue/archive", } @Article{Butcher:1961:PTP, author = "J. C. Butcher", title = "A Partition Test for Pseudo-Random Numbers (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "15", number = "74", pages = "198--199", month = apr, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", HDnumber = "10", journal-URL = "http://www.ams.org/mcom/", } @Article{Butcher:1961:RSN, author = "J. C. Butcher", title = "Random sampling from the normal distribution", journal = j-COMP-J, volume = "3", number = "4", pages = "251--253", month = jan, year = "1961", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:55:25 MDT 2000", bibsource = "Distributed/QLD.bib; Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_04/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_04/030251.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_04/tiff/251.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_04/tiff/252.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_04/tiff/253.tif", acknowledgement = ack-nhfb, date = "13/05/93", descriptors = "RVG", enum = "7085", fjournal = "The Computer Journal", HDnumber = "11", journal-URL = "http://comjnl.oxfordjournals.org/", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Corrsin:1961:CLS, author = "S. Corrsin and O. M. Phillips", title = "Contour Length and Surface Area of Multiple-Valued Random Variables", journal = j-J-SIAM, volume = "9", number = "3", pages = "395--404", month = sep, year = "1961", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Article{Fisser:1961:STA, author = "H. Fisser", title = "Some tests applied to pseudo-random numbers generated by {v. H{\"o}rner}'s rule", journal = j-NUM-MATH, volume = "3", pages = "247--249", month = dec, year = "1961", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Sun Oct 17 19:01:15 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", HDnumber = "28", journal-URL = "http://link.springer.com/journal/211", } @Article{Greenberger:1961:NNP, author = "Martin Greenberger", title = "Notes on a New Pseudo-Random Number Generator", journal = j-J-ACM, volume = "8", number = "2", pages = "163--167", month = apr, year = "1961", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321062.321065", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Dec 05 20:05:28 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, annote = "The IBM RNG!", descriptors = "RNG; linear congruential generator", fjournal = "Journal of the Association for Computing Machinery", HDnumber = "41", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Greenberger:1961:PDS, author = "Martin Greenberger", title = "An a Priori Determination of Serial Correlation in Computer Generated Random Numbers", journal = j-MATH-COMPUT, volume = "15", number = "76", pages = "383--389", month = oct, year = "1961", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", note = "See also corrigenda, Math. Comp. {\bf 16} (1962), p. 126.", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", HDnumber = "42", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Herrmann:1961:SER, author = "R. G. Herrmann", title = "The Statistical Evaluation of Random Number Generating Sequences for Digital Computers", type = "Report", number = "APEX - 635", institution = "General Electric Co.", address = "????", year = "1961", bibdate = "Mon Jan 16 22:38:45 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "U.S. Dept. of Commerce, Office of Technical Services.", acknowledgement = ack-nhfb, } @Article{Hlawka:1961:FBV, author = "Edmund Hlawka", title = "{Funktionen von beschr{\"a}nkter Variation in der Theorie der Gleichverteilung}. ({German}) [{Functions} of bounded variation in the theory of uniform distribution]", journal = j-ANN-MAT-PURA-APPL-4, volume = "54", number = "??", pages = "325--333", month = "????", year = "1961", CODEN = "ANLMAE", ISSN = "0003-4622", MRclass = "10.33 (10.50)", MRnumber = "0139597 (25 \#3029)", MRreviewer = "W. J. LeVeque", bibdate = "Thu Jan 19 08:35:26 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Annali di matematica pura ed applicata. Series 4", language = "German", } @Article{Kiefer:1961:LDE, author = "J. Kiefer", title = "On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm", journal = j-PAC-J-MATH, volume = "11", number = "??", pages = "649--660", month = "????", year = "1961", CODEN = "PJMAAI", ISSN = "0030-8730 (print), 1945-5844 (electronic)", ISSN-L = "0030-8730", bibdate = "Tue Dec 27 11:15:50 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Pacific Journal of Mathematics", journal-URL = "http://msp.org/pjm", } @Article{Kuehn:1961:BPR, author = "Heidi G. Kuehn", title = "A $ 48 $-bit pseudo-random number generator", journal = j-CACM, volume = "4", number = "8", pages = "350--352", month = aug, year = "1961", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "68.00", MRnumber = "26\#2034", bibdate = "Fri Nov 25 18:19:34 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A new 48-bit pseudo-random number generator, suitable for several computers, was tested statistically for randomness to determine its adequacy for use in Monte Carlo programs. Frequency tests, distributions of certain low-order moments, runs up and down, and runs above and below the mean were applied to one-half million generated numbers lying within the interval $ (0, 1) $ and to three sets of integers obtained from specified bits within the generated numbers. These tests substantiated the randomness of all numbers except for the set of integers coming from the least significant bits.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", HDnumber = "66", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", ZMreviewer = "M. E. Muller", } @Article{Liniger:1961:MDH, author = "Werner Liniger", title = "On a Method by {D. H. Lehmer} for the Generation of Pseudo Random Numbers", journal = j-NUM-MATH, volume = "3", pages = "265--270", month = dec, year = "1961", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Tue Dec 21 16:29:06 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", HDnumber = "71", journal-URL = "http://link.springer.com/journal/211", } @Article{Mamangakis:1961:MNR, author = "S. E. Mamangakis", title = "Mathematical Notes: Remarks on the {Fibonacci} Series Modulo $m$", journal = j-AMER-MATH-MONTHLY, volume = "68", number = "7", pages = "648--649", month = aug # "\slash " # sep, year = "1961", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:24 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", HDnumber = "74", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Manelis:1961:GRN, author = "J. B. Manelis", title = "Generating random noise", journal = j-ELECTRONICS, volume = "??", number = "??", pages = "66--69", day = "8", month = sep, year = "1961", ISSN = "0883-4989", bibdate = "Thu Feb 02 17:48:27 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Electronics", } @Article{Marsaglia:1961:ERV, author = "G. Marsaglia", title = "Expressing a random variable in terms of uniform random variables", journal = j-ANN-MATH-STAT, volume = "32", number = "3", pages = "894--898", month = sep, year = "1961", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177704983", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "65.15", MRnumber = "23 \#B3122", MRreviewer = "M. E. Muller", bibdate = "Thu Dec 22 07:41:29 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", URL = "http://projecteuclid.org/euclid.aoms/1177704983; http://www.jstor.org/stable/2237849", ZMnumber = "0139.35604", abstract = "This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is to choose a distribution function which is close to the original and use it most of the time, applying the correction only infrequently. Mixtures allow this to be done in probability terms rather than in the more elaborate ways of conventional numerical analysis, which must be applied every time.", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "75", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", keywords = "probability theory", } @Article{Marsaglia:1961:GER, author = "G. Marsaglia", title = "Generating exponential random variables", journal = j-ANN-MATH-STAT, volume = "32", number = "3", pages = "899--900", month = sep, year = "1961", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177704984", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "65.15", MRnumber = "23 \#B3123", MRreviewer = "M. E. Muller", bibdate = "Thu Dec 22 07:41:41 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", URL = "http://projecteuclid.org/euclid.aoms/1177704984; http://www.jstor.org/stable/2237850", ZMnumber = "0139.35603", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", HDnumber = "76", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", keywords = "probability theory", } @TechReport{Marsaglia:1961:PGN, author = "George Marsaglia", title = "Procedures for Generating Normal Random Variables, {II}", type = "Mathematical note", number = "243", institution = "Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", month = oct, year = "1961", bibdate = "Tue Jun 21 18:56:22 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A method for generating a normal random variable in terms of uniform random variables is described. The method is based on representing a density function as a mixture of simpler densities. It is fast and requires little storage (60 constants). It is not quite as fast as other methods, but it is simpler, with less chance for prospective users being set adrift in a sea of details", acknowledgement = ack-nhfb, HDnumber = "78", } @TechReport{Marsaglia:1961:RGR, author = "G. Marsaglia", title = "Remark on generating a random variable having a nearly linear density function", type = "Mathematical Note", number = "242", institution = "Boeing Scientific Research Labs", address = "Seattle, WA, USA", year = "1961", bibdate = "Mon Jun 27 15:17:02 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "77", } @Article{Marsaglia:1961:SPT, author = "George Marsaglia", title = "Some probability theory associated with clustered-rocket flights", journal = j-PLANET-SPACE-SCI, volume = "4", number = "??", pages = "194--201", month = jan, year = "1961", CODEN = "PLSSAE", DOI = "https://doi.org/10.1016/0032-0633(61)90132-5", ISSN = "0032-0633 (print), 1873-5088 (electronic)", ISSN-L = "0032-0633", bibdate = "Wed Jun 22 06:45:09 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.sciencedirect.com/science/article/pii/0032063361901325", abstract = "The primary purpose of this note is to provide the probability distribution of the amount of propellant remaining in a cluster of rocket engines at the times that the first and second burnouts occur. In addition, various other random variables associated with the random behavior of the engines of a cluster (pitch and yaw moments, time between successive burnouts, etc.) are discussed.", acknowledgement = ack-nhfb, fjournal = "Planetary and Space Science", journal-URL = "http://www.sciencedirect.com/science/journal/00320633", } @Book{Orcutt:1961:MSS, author = "Guy H. Orcutt and Martin Greenberger and John Korbel and Alice M. Rivlin", title = "Microanalysis of socioeconomic systems; a simulation study", publisher = "Harper", address = "New York, NY, USA", pages = "xviii + 425", year = "1961", LCCN = "H61 .O7", bibdate = "Mon Jun 27 15:30:08 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, HDnumber = "91", remark = "First of a series relating to the work of the Social Systems Research Institute at the University of Wisconsin.", subject = "Social sciences; Simulation methods; United States; Population; Working class", } @Article{Peach:1961:BPR, author = "Paul Peach", title = "Bias in pseudo-random numbers", journal = j-J-AM-STAT-ASSOC, volume = "56", number = "295", pages = "610--618", month = sep, year = "1961", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2282083", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", HDnumber = "97", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Pinkham:1961:DFS, author = "Roger S. Pinkham", title = "On the Distribution of First Significant Digits", journal = j-ANN-MATH-STAT, volume = "32", number = "4", pages = "1223--1230", month = dec, year = "1961", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177704862", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Sat May 31 09:10:59 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/annmathstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T; http://projecteuclid.org/euclid.aoms/1177704862; http://www.jstor.org/stable/2237922", abstract = "It has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From p. 1223: ``\ldots{} the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $.''\par \ldots{} ``The only distribution for first significant digits which is invariant under scale change of the underlying distribution is $ \log_{10}(n + 1) $. Contrary to suspicion this is a non-trivial mathematical result, for the variable $n$ is discrete.''.\par From p. 1230: ``The foregoing results bear on questions of round-off in computing machines. Since $ d(u v) = u d v + v d u $, the error resulting from multiplying two rounded numbers will be governed primarily by the first significant digits of the two numbers being multiplied. Now the distribution of first significant digits, favoring as it does low order digits, tends to produce less error than would be the case if first significant digits were uniform as has sometimes been assumed.''\par Cited in \cite{Sterbenz:1974:FPC}.", } @Article{Rao:1961:GRP, author = "C. Radhakrishna Rao", title = "Generation of random permutations of given number of elements using random sampling numbers", journal = j-SANKHYA-A, volume = "23", number = "??", pages = "305--307", year = "1961", CODEN = "SANABS", ISSN = "0036-4452", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", HDnumber = "101", } @InProceedings{Richtmyer:1961:MCM, author = "R. D. Richtmyer", title = "{Monte Carlo} methods", crossref = "Birkhoff:1961:NRT", pages = "190--205", year = "1961", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "104", } @Article{Riffenburgh:1961:RPI, author = "Robert H. Riffenburgh", title = "Recent Publications: {{\em Introduction to Probability and Random Variables}}, by {George P. Wadsworth and Joseph G. Bryan}", journal = j-AMER-MATH-MONTHLY, volume = "68", number = "5", pages = "518--518", month = may, year = "1961", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:19 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Sibuya:1961:EOR, author = "Masaaki Sibuya", title = "On exponential and other random variable generators", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "13", number = "1", pages = "231--237", month = dec, year = "1961", CODEN = "AISXAD", DOI = "https://doi.org/10.1007/BF02868873", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", bibdate = "Sat Jan 31 16:59:46 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://link.springer.com/article/10.1007/BF02868873", acknowledgement = ack-nhfb, fjournal = "Annals of the Institute of Statistical Mathematics", journal-URL = "http://link.springer.com/journal/10463", } @Book{Solomon:1961:SIA, editor = "Herbert Solomon", title = "Studies in item analysis and prediction", volume = "6", publisher = pub-STANFORD, address = pub-STANFORD:adr, pages = "310", year = "1961", LCCN = "BF39 .S64", bibdate = "Mon Jun 27 15:52:30 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "With contributions by Rosedith Sitgreaves and others.", series = "Stanford mathematical studies in the social sciences", acknowledgement = ack-nhfb, HDnumber = "112", subject = "Psychometrics; Prediction (Psychology); Psychological tests", } @Book{Wendel:1961:LMC, author = "James G. Wendel", title = "Lectures on {Monte Carlo}: University of Michigan Summer Session Courses on Numerical Analysis", publisher = pub-U-MICHIGAN, address = pub-U-MICHIGAN:adr, pages = "??--??", year = "1961", LCCN = "????", bibdate = "Mon Jun 27 16:25:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "139", } @Article{Wouk:1961:DDR, author = "Arthur Wouk", title = "On Digit Distributions for Random Variables", journal = j-J-SIAM, volume = "9", number = "4", pages = "597--603", month = dec, year = "1961", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Article{Barnett:1962:BPR, author = "V. D. Barnett", title = "The Behavior of Pseudo-Random Sequences Generated on Computers by the Multiplicative Congruential Method", journal = j-MATH-COMPUT, volume = "16", number = "77", pages = "63--69", month = jan, year = "1962", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/pdfplus/2003811.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", HDnumber = "1", journal-URL = "http://www.ams.org/mcom/", } @Article{Behrenz:1962:AR, author = "Peter G. Behrenz", title = "{Algorithm 133}: {RANDOM}", journal = j-CACM, volume = "5", number = "11", pages = "553--553", month = nov, year = "1962", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:42 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Behrenz:1962:RAR, author = "Peter G. Behrenz", title = "Remark on {Algorithm 133}: {Random}", journal = j-CACM, volume = "5", number = "12", pages = "606--606", month = dec, year = "1962", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:43 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Clark:1962:CMM, author = "G. Miller Clark", title = "Corrections to {Mervin E. Muller, {\em A Note on a Method for Generating Points Uniformly on $N$-Dimensional Spheres}}", journal = j-MATH-COMPUT, volume = "16", number = "78", pages = "261--261", year = "1962", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Mon Jun 27 14:07:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Muller:1959:NMG}.", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", HDnumber = "2'", journal-URL = "http://www.ams.org/mcom/", } @Article{Dillard:1962:EGR, author = "G. M. Dillard and R. E. Simmons", title = "An Electronic Generator of Random Numbers", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-11", number = "2", pages = "284--284", month = apr, year = "1962", CODEN = "IRELAO", DOI = "https://doi.org/10.1109/TEC.1962.5219362", ISSN = "0367-9950", bibdate = "Thu Jul 14 09:11:50 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See comments \cite{Barnes:1963:CEG}.", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219362", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885", } @Article{Fan:1962:DSP, author = "C. T. Fan and Mervin E. Muller and Ivan Rezucha", title = "Development of Sampling Plans by Using Sequential (Item by Item) Selection Techniques and Digital Computers", journal = j-J-AM-STAT-ASSOC, volume = "57", number = "298", pages = "387--402", month = jun, year = "1962", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:36 MST 2012", bibsource = "Database/Wiederhold.bib; http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314179; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2281647", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", remark = "The authors discuss an algorithm for sampling $n$ of $N$ values, with time cost $ O(N) $. See \cite{Rouzankin:1999:CAR} for a discussion of this algorithm, and others, one with storage cost $ O(N) $ and time $ O(n) $, a second with storage cost $ O(n) $ and time cost $ O(n^2) $, and more complex algorithms with time cost $ O(n \log n) $ and $ O(n) $. See also \cite{Bentley:1980:GSL} for a short algorithm with worst case time $ O(n) $ with storage $ O(1) $ (with immediate output) or $ O(n) $ with array output, and the selected values are sorted.", } @Article{Foster:1962:MRS, author = "Malcolm B. Foster", title = "A method of representation, storage and retrieval of $ 13 $ random codes in a $4$-digit number or $ 16 $ random codes in a $5$-digit number", journal = j-CACM, volume = "5", number = "3", pages = "165--165", month = mar, year = "1962", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:37 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @TechReport{Franklin:1962:DSR, author = "Joel N. Franklin", title = "Deterministic simulation of random processes", type = "Technical Report", number = "118", institution = "Computing Center, California Institute of Technology", address = "Pasadena, CA, USA", year = "1962", bibdate = "Mon Jun 27 16:38:27 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "3'", } @InBook{Galler:1962:RNG, author = "Bernard A. Galler", booktitle = "The Language of Computers", title = "Random number generators", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, bookpages = "x + 244", pages = "56--59", year = "1962", LCCN = "QA76.5 .G3", bibdate = "Mon Jan 16 22:35:27 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, subject = "MAD (Computer program language); Programming languages (Electronic computers)", } @Article{Gordon:1962:SND, author = "Basil Gordon and W. H. Mills and L. R. Welch", title = "Some new difference sets", journal = j-CAN-J-MATH, volume = "14", number = "??", pages = "614--625", month = "????", year = "1962", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1962-052-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:31 MDT 2011", bibsource = "http://cms.math.ca/cjm/v14/; https://www.math.utah.edu/pub/tex/bib/canjmath1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Book{Hamming:1962:NMS, author = "R. W. (Richard Wesley) Hamming", title = "Numerical methods for scientists and engineers", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xvii + 411", year = "1962", LCCN = "QA297 .H28", MRclass = "65.00", MRnumber = "0137279", MRreviewer = "G. E. Forsythe", bibdate = "Mon Aug 6 07:24:38 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "International Series in Pure and Applied Mathematics", acknowledgement = ack-nhfb, HDnumber = "51", remark = "Cited in \cite{Sterbenz:1974:FPC}.", subject = "Numerical analysis; Electronic digital computers; random numbers", tableofcontents = "1. The difference calculus \\ 2. Roundoff noise \\ 3. The summation calculus \\ 4. Evaluation of infinite series \\ 5. Finite difference equations \\ 6. The finite Fourier series \\ 7--9. Polynomial approximation introduction \\ 10. A uniform method for finding formulas \\ 11. On finding the error term of a formula \\ 12. Formulas for definite integrals \\ 13. Indefinite integrals \\ 14. Introduction to differential equations \\ 15. A general theory of predictor-corrector methods \\ 16. Special methods of integrating ordinary differential equations \\ 17--18. Least squares theory and practice \\ 19. Chebyshev polynomials \\ 20. Rational functions \\ 21--22. Periodic functions --- Fourier series \\ 23. Nonperiodic functions --- the Fourier integral \\ 24. Linear filters --- smoothing and differentiating \\ 25. Integrals and differential equations \\ 26. Exponential approximation \\ 27. Singularities \\ 28. On finding zeros \\ 29. Simultaneous linear algebraic equations \\ 30. Inversion of matrices and eigenvalues \\ 31. Some examples of the simulation of situations and processes \\ 32. Random numbers and Monte Carlo methods \\ $N+1$: The art of computing for scientists and engineers", } @Article{Hlawka:1962:ABM, author = "Edmund Hlawka", title = "{Zur angen{\"a}herten Berechnung mehrfacher Integrale}. ({German}) [{Toward} approximate calculation of multiple integrals]", journal = j-MONAT-MATH, volume = "66", number = "2", pages = "140--151", month = apr, year = "1962", CODEN = "MNMTA2", DOI = "https://doi.org/10.1007/BF01387711", ISSN = "0026-9255 (print), 1436-5081 (electronic)", ISSN-L = "0026-9255", MRclass = "65.55", MRnumber = "0143329 (26 \#888)", MRreviewer = "J. F. Koksma", bibdate = "Thu Jan 19 08:38:21 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/content/g5m4457x5525866p/", acknowledgement = ack-nhfb, fjournal = "Monatshefte f{\"u}r Mathematik", journal-URL = "http://link.springer.com/journal/605", language = "German", } @Article{Hull:1962:RNG, author = "T. E. Hull and A. R. Dobell", title = "Random Number Generators", journal = j-SIAM-REVIEW, volume = "4", number = "3", pages = "230--254", month = jul, year = "1962", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1004061", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Wed Jun 22 07:53:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://link.aip.org/link/?SIR/4/230/1; https://dspace.library.uvic.ca:8443/bitstream/handle/1828/3142/Random_Number_Generators.pdf?sequence=3", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @TechReport{Marsaglia:1962:FPG, author = "G. Marsaglia and M. D. Maclaren and T. A. Bray", title = "A Fast Procedure for Generating Normal Random Variables", type = "Mathematical note", number = "282", institution = "Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", month = aug, year = "1962", bibdate = "Tue Jun 21 18:58:31 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=AD0296195", abstract = "A discussion is given of the generation of normal random variables very rapidly in a computer --- for example, at the rate of 10,000--15,000 per second in the IBM 7090. The method is suitable for any computer. The incorporation of successive improvements has led to a procedure which is fairly easy to program, requires little storage, 300--400 constants, is very fast (it takes about as long to generate the normal $x$ as the uniform $u$ from which it comes), and is completely accurate, in the sense that in theory the procedure returns a random variable with exactly the required distribution; in practice the result is an approximation influenced only by the capacity (word length) of the computer.", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1962:IPM, author = "George Marsaglia", title = "Improving the Polar Method for Generating a Pair of Normal Random Variables", type = "Technical report", number = "D1-82-0203", institution = "Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", month = sep, year = "1962", bibdate = "Tue Jun 21 18:17:38 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1962:RVC, author = "George Marsaglia", title = "Random Variables and Computers", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "??", month = may, year = "1962", bibdate = "Wed Nov 12 07:29:32 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0278358", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1962:SPG, author = "George Marsaglia and T. A. Bray", title = "A small procedure for generating normal random variables", type = "Mathematical note", number = "283", institution = "Boeing Scientific Research Labs", address = "Seattle, WA, USA", pages = "??", month = nov, year = "1962", bibdate = "Wed Jun 22 09:24:42 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{MendesFrance:1962:CMF, author = "M. {Mend{\`e}s France}", title = "Calcul des moyennes des fonctions al{\'e}atoires ou pseudo-al{\'e}atoires par {\'e}chantillonnage. ({French}) [Averaging functions of random or pseudo-random sampling]", journal = "Publ. Inst. Statist. Univ. Paris", volume = "11", number = "??", pages = "225--256", month = "????", year = "1962", CODEN = "????", ISSN = "????", MRnumber = "MR 150793", bibdate = "Thu Jan 19 07:14:23 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "", acknowledgement = ack-nhfb, language = "French", } @Article{Pathria:1962:SSR, author = "R. K. Pathria", title = "A Statistical Study of Randomness Among the First $ 10, 000 $ Digits of $ \pi $", journal = j-MATH-COMPUT, volume = "16", number = "78", pages = "188--197", month = apr, year = "1962", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", HDnumber = "5'", journal-URL = "http://www.ams.org/mcom/", } @Article{Richtmyer:1962:CFE, author = "R. D. Richtmyer and Marjorie Devaney and N. Metropolis", title = "Continued fraction expansions of algebraic numbers", journal = j-NUM-MATH, volume = "4", pages = "68--84", month = dec, year = "1962", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "10.09", MRnumber = "MR0136574 (25 \#44)", MRreviewer = "H. Cohn", bibdate = "Thu Dec 22 07:42:20 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0101.28101", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", HDnumber = "105", journal-URL = "http://link.springer.com/journal/211", } @Article{Scheuer:1962:GNR, author = "E. M. Scheuer and D. S. Stoller", title = "On the Generation of Normal Random Vectors", journal = j-TECHNOMETRICS, volume = "4", number = "??", pages = "278--281", month = "????", year = "1962", CODEN = "TCMTA2", ISSN = "0040-1706 (print), 1537-2723 (electronic)", ISSN-L = "0040-1706", bibdate = "Thu Jan 05 10:58:18 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Technometrics", journal-URL = "http://www.jstor.org/journals/00401706.html; http://www.tandfonline.com/loi/utch20", } @Article{Shanks:1962:CD, author = "Daniel Shanks and John W. {Wrench, Jr.}", title = "Calculation of $ \pi $ to 100,000 Decimals", journal = j-MATH-COMPUT, volume = "16", number = "77", pages = "76--99", month = jan, year = "1962", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", HDnumber = "110", journal-URL = "http://www.ams.org/mcom/", } @Article{Sibuya:1962:FCN, author = "Masaaki Sibuya", title = "Further consideration on normal random variable generator", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "14", number = "1", pages = "159--165", month = dec, year = "1962", CODEN = "AISXAD", DOI = "https://doi.org/10.1007/BF02868636", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", bibdate = "Sat Jan 31 16:59:47 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://link.springer.com/article/10.1007/BF02868636", acknowledgement = ack-nhfb, fjournal = "Annals of the Institute of Statistical Mathematics", journal-URL = "http://link.springer.com/journal/10463", } @Article{Spanier:1962:UAM, author = "J. Spanier", title = "A Unified Approach to {Monte Carlo} methods and an Application to a Multigroup Calculation of Absorption Rates", journal = j-SIAM-REVIEW, volume = "4", number = "2", pages = "115--134", month = apr, year = "1962", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1004030", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:04:51 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/4/2; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://www.jstor.org/stable/2028365", acknowledgement = ack-nhfb, fjournal = "SIAM Review", HDnumber = "113", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "April 1962", } @Book{Todd:1962:SNA, editor = "John Todd", title = "Survey of Numerical Analysis", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xvi + 589", year = "1962", LCCN = "????", bibdate = "Mon Jun 27 16:07:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, HDnumber = "126", } @Book{Walsh:1962:HNS, author = "J. E. Walsh", title = "Handbook of Nonparametric Statistics", publisher = "Van Nostrand", address = "Princeton, NJ, USA", pages = "xxvi + 549", year = "1962", LCCN = "QA278.8 .W34", bibdate = "Mon Jan 16 22:37:08 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, keywords = "Tests of randomness", } @Article{Allard:1963:MCR, author = "J. L. Allard and A. R. Dobell and T. E. Hull", title = "Mixed Congruential Random Number Generators for Decimal Machines", journal = j-J-ACM, volume = "10", number = "2", pages = "131--141", month = apr, year = "1963", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321160.321163", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Sat Nov 05 22:55:28 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", xxmonth = "none", xxnumber = "none", } @Article{Anonymous:1963:BRBd, author = "Anonymous", title = "Book Review: {{\booktitle{Random Variables and Probability Distributions}} by H. Cram{\'e}r}", journal = j-BIOMETRIKA, volume = "50", number = "1/2", pages = "232--233", month = jun, year = "1963", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2333784", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 14:33:11 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315447; https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2333784", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://www.jstor.org/journals/00063444.html", } @Article{Barnes:1963:CEG, author = "George H. Barnes", title = "Comment on {``An Electronic Generator of Random Numbers''}", journal = j-IEEE-TRANS-ELEC-COMPUT, volume = "EC-12", number = "1", pages = "22--22", month = feb, year = "1963", CODEN = "IEECA8", DOI = "https://doi.org/10.1109/PGEC.1963.263393", ISSN = "0367-7508", bibdate = "Thu Jul 14 08:10:36 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Dillard:1962:EGR}.", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037766", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electronic Computers", } @Article{Bolshev:1963:APT, author = "L. N. Bol'shev", title = "Asymptotically {Pearson} Transformations", journal = j-THEORY-PROBAB-APPL, volume = "8", number = "2", pages = "121--146", month = "????", year = "1963", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/1108012", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Tue Apr 1 10:34:47 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/8/2; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", onlinedate = "January 1963", } @Article{DeMatteis:1963:SAP, author = "A. {De Matteis} and B. Faleschini", title = "Some arithmetical properties in connection with pseudo-random numbers", journal = j-BOLL-UNIONE-MAT-ITAL, volume = "18", number = "??", pages = "171--184", month = "????", year = "1963", CODEN = "BLUMAM", ISSN = "0041-7084", bibdate = "Fri Jan 6 10:17:45 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Bollettino della Unione matematica italiana", } @Article{Firestone:1963:CNU, author = "C. D. Firestone and J. E. Hanson", title = "Classroom Notes: Uncorrelated {Gaussian} Dependent Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "70", number = "6", pages = "659--660", month = jun # "\slash " # jul, year = "1963", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:09 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Book{Fisher:1963:STB, author = "{Sir} Ronald Aylmer Fisher and Frank Yates", title = "Statistical Tables for Biological, Agricultural and Medical Research", publisher = pub-OLIVER-BOYD, address = pub-OLIVER-BOYD:adr, edition = "Sixth", pages = "x + 146", year = "1963", ISBN = "0-05-000872-2, 0-582-44525-6", ISBN-13 = "978-0-05-000872-0, 978-0-582-44525-3", LCCN = "QH324 .F52 1963", bibdate = "Mon Jun 29 11:28:52 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fisher-ronald-aylmer.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "Sir Ronald Aylmer Fisher (17 February 1890--29 July 1962)", remark = "This book contains one of the early pre-computer tabulations of pseudorandom numbers.", subject = "Statistics; Charts, diagrams, etc", xxaddress = "Burnt Mill, UK", xxpublisher = "Longman", } @Article{Franklin:1963:DSR, author = "Joel N. Franklin", title = "Deterministic Simulation of Random Processes", journal = j-MATH-COMPUT, volume = "17", number = "81", pages = "28--59", month = jan, year = "1963", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/2003733", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Gabai:1963:DCSa, author = "H. Gabai", title = "On the discrepancy of certain sequences $ \bmod 1 $", journal = "Nederl. Akad. Wetensch. Proc. Ser. A", volume = "66", number = "??", pages = "603--605", month = "????", year = "1963", CODEN = "????", ISSN = "????", bibdate = "Thu Jan 19 06:46:36 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "Zbl 0129.03102", acknowledgement = ack-nhfb, fjournal = "Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae", } @Article{Gabai:1963:DCSb, author = "H. Gabai", title = "On the discrepancy of certain sequences $ \bmod 1 $", journal = j-INDAG-MATH, volume = "25", number = "??", pages = "603--605", month = "????", year = "1963", CODEN = "IMTHBJ", ISSN = "0019-3577, 0023-3358", ISSN-L = "0019-3577", MRnumber = "MR 155812", bibdate = "Thu Jan 19 06:46:36 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Indagationes Mathematic{\ae}", } @Article{George:1963:ANR, author = "R. George", title = "{Algorithm 200}: {Normal} Random", journal = j-CACM, volume = "6", number = "8", pages = "444", month = aug, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:31:40 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See also \cite{Pike:1965:CAGb}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Gill:1963:WDP, author = "Arthur Gill", title = "On a Weight Distribution Problem, with Application to the Design of Stochastic Generators", journal = j-J-ACM, volume = "10", number = "1", pages = "110--122", month = jan, year = "1963", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321150.321159", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Sat Nov 05 22:55:28 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Hoeffding:1963:PIS, author = "Wassily Hoeffding", title = "Probability inequalities for sums of bounded random variables", journal = j-J-AM-STAT-ASSOC, volume = "58", number = "301", pages = "13--30", month = mar, year = "1963", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Fri Jan 6 09:58:25 2012", bibsource = "Ai/colt.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2282952", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Jagerman:1963:AFS, author = "David L. Jagerman", title = "The autocorrelation function of a sequence uniformly distributed modulo $1$", journal = j-ANN-MATH-STAT, volume = "34", number = "4", pages = "1243--1252", month = dec, year = "1963", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Mon Jan 16 22:32:42 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2238334", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Kolmogorov:1963:TRN, author = "A. N. Kolmogorov", title = "On tables of random numbers", journal = j-SANKHYA-A, volume = "25", number = "??", pages = "369--376", month = "????", year = "1963", CODEN = "SANABS", ISSN = "0036-4452", bibdate = "Mon Jan 16 22:33:13 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", } @Article{Laughlin:1963:RAR, author = "Donald L. Laughlin", title = "Remark on {Algorithm 133}: {Random}", journal = j-CACM, volume = "6", number = "3", pages = "105--105", month = mar, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:45 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @TechReport{MacLaren:1963:FPG, author = "M. D. MacLaren and G. Marsaglia and T. A. Bray", title = "A Fast Procedure for Generating Exponential Random Variables", type = "Report", number = "??", institution = "Boeing Scientific Research Labs", address = "Seattle, WA, USA", pages = "??", month = jan, year = "1963", bibdate = "Tue Jun 21 18:58:31 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A very fast method for generating exponential random variables in a digital computer is presented. The method is exact, in the sense that in theory it returns a random variable with exactly the exponential distribution. In practice the result is an approximation, but the accuracy of the approximation depends only on the word length of the computer.", acknowledgement = ack-nhfb, remark = "Published in \cite{MacLaren:1964:FPG}.", } @TechReport{Magleby:1963:SNF, author = "K. B. Magleby", title = "The synthesis of nonlinear feedback shift registers", type = "Report", number = "TR 6207-1", institution = "Stanford Electronics Laboratory", address = "Stanford, CA, USA", year = "1963", bibdate = "Tue Feb 07 11:14:29 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Marsaglia:1963:GDR, author = "G. Marsaglia", title = "Generating discrete random variables in a computer", journal = j-CACM, volume = "6", number = "1", pages = "37--38", month = jan, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:44 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, country = "USA", descriptors = "RVG", enum = "7628", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", location = "SEL: Wi", references = "0", revision = "16/01/94", } @TechReport{Marsaglia:1963:RNF, author = "George Marsaglia", title = "Random numbers fall mainly in the planes", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "9", month = aug, year = "1963", bibdate = "Wed Nov 12 07:42:28 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0685578", abstract = "Most of the world's computer centers use congruential random number generators. This note points out that such random number generators produce points in $ 2, 3, 4, \ldots {} $ dimensions which are too regular for many Monte Carlo calculations. The trouble is that the points fall exactly on a lattice with quite a gross structure. The paper gives details of the degree of regularity of such generators in terms of sets of relatively few parallel hyperplanes which contain all of the points produced by the generator.", acknowledgement = ack-nhfb, } @Book{Moses:1963:TRP, author = "Lincoln E. Moses and Robert V. Oakford", title = "Tables of random permutations", publisher = pub-STANFORD, address = pub-STANFORD:adr, pages = "233", year = "1963", LCCN = "QA165 .M6", bibdate = "Thu Mar 1 08:41:02 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Permutations; Tables; Stochastic processes", } @Article{Poore:1963:CAR, author = "Jesse H. {Poore, Jr.}", title = "Certification of {Algorithm 133}: {Random}", journal = j-CACM, volume = "6", number = "4", pages = "167--167", month = apr, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:46 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Tucker:1963:QCS, author = "Howard G. Tucker", title = "Quasi-Convergent Series of Independent Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "70", number = "7", pages = "718--722", month = aug # "\slash " # sep, year = "1963", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:11 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Ahsanullah:1964:RVE, author = "Mohammad Ahsanullah", title = "Record values of exponentially distributed random variables", journal = j-STAT-PAPERS, volume = "22", number = "2", pages = "121--127", month = jun, year = "1964", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/BF02933548", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:11:57 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/BF02933548", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{Alanen:1964:TFF, author = "J. D. Alanen and Donald E. Knuth", title = "Tables of finite fields", journal = j-SANKHYA-A, volume = "26", number = "??", pages = "305--328", year = "1964", CODEN = "SANABS", ISSN = "0036-4452", MRclass = "12.20 (33.00)", MRnumber = "32 #4122", MRreviewer = "J. J. Stone", bibdate = "Fri Mar 22 18:03:29 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", } @Article{Bekessy:1964:RBD, author = "Andr{\'a}s B{\'e}k{\'e}ssy", title = "Remarks on beta distributed random numbers", journal = "Magyar Tud. Akad. Mat. Kutat{\'o} Int. K{\"o}zl.", volume = "9", pages = "565--571", year = "1964", MRclass = "65.15", MRnumber = "MR0195232 (33 #3435)", MRreviewer = "J. H. Halton", bibdate = "Thu Mar 8 21:21:07 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, remark = "Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Series B, Fascicle 4", } @Article{Brillinger:1964:BRI, author = "David R. Brillinger", title = "Book Reviews: {{\em Information and Information Stability of Random Variables and Processes}}, by {M. S. Pinsker} and {Amiel Feinstein}", journal = j-APPL-STAT, volume = "13", number = "2", pages = "134--135", year = "1964", CODEN = "APSTAG", ISSN = "0035-9254 (print), 1467-9876 (electronic)", ISSN-L = "0035-9254", bibdate = "Sat Apr 21 10:18:17 MDT 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Applied Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues", } @TechReport{Chow:1964:RNG, author = "D. K. Chow", title = "Random number generator test procedures applied to a modified, multiplicative, congruential generator method", number = "UIUCDCS-R-1964-612", institution = "Department of Computer Science, University of Illinois at Urbana-Champaign", address = "Urbana, Illinois", year = "1964", bibdate = "Tue Mar 06 20:45:41 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Durstenfeld:1964:ARP, author = "Richard Durstenfeld", title = "{Algorithm 235}: {Random} permutation", journal = j-CACM, volume = "7", number = "7", pages = "420--420", month = jul, year = "1964", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/364520.364540", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:54 MST 2005", bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Esmenjaud-Bonnardel:1964:PGN, author = "M. Esmenjaud-Bonnardel", title = "Un proc{\'e}d{\'e} de g{\'e}n{\'e}ration de nombres `pseudo-al{\'e}atoires' pour {CAB 500}. ({French}) [{A} procedure for the generation of pseudorandom numbers on the {CAB 500}]", journal = j-CHIFFRES, volume = "7", number = "??", pages = "185--197", month = "????", year = "1964", CODEN = "????", ISSN = "0245-9922", bibdate = "Mon Jan 16 22:28:42 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Chiffres: Revue de l'Association fran{\c{c}}aise de Calcul", language = "French", xxISSN = "0556-7823", xxjournal = "Revue Fran{\c{c}}aise de Traitement de l'Information", } @Article{Gebhardt:1964:GND, author = "Friedrich Gebhardt", title = "Generating Normally Distributed Random Numbers by Inverting the Normal Distribution Function (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "18", number = "86", pages = "302--306", month = apr, year = "1964", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "Distributed/QLD.bib; Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7308", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Halton:1964:ARI, author = "J. H. Halton", title = "{Algorithm 247}: {Radical}-inverse quasi-random point sequence", journal = j-CACM, volume = "7", number = "12", pages = "701--702", month = dec, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:57 MST 2005", bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Hammer:1964:GRN, author = "C. Hammer and L. Green", title = "Generation of Random Numbers", journal = "Instruments and Control Systems", volume = "37", number = "5", pages = "149--150", month = "????", year = "1964", CODEN = "INCSA7", ISSN = "0020-4404", bibdate = "Mon Jan 16 22:29:24 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Book{Hammersley:1964:MCM, author = "J. M. Hammersley and D. C. Handscomb", title = "{Monte Carlo} methods", publisher = "Methuen", address = "London, UK", pages = "vii + 178", year = "1964", LCCN = "QA273 .H354 1964", bibdate = "Fri Jan 06 10:30:48 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Methuen's monographs on applied probability and statistics", acknowledgement = ack-nhfb, remark = "Co-published by Wiley.", tableofcontents = "1. The general nature of Monte Carlo methods \\ 2. Short resume of statistical terms \\ 3. Random, pseudorandom, and quasirandom numbers \\ 4. Direct simulation \\ S. General principles of the Monte Carlo method \\ 6. Conditioned Monte Carlo \\ 7. Solution of linear operator equations \\ 8. Radiation shielding and reactor criticality \\ 9. Problems in statistical mechanics \\ 10. Long polymer molecules \\ 11. Percolation processes \\ 12. Multivariate problems", } @Article{Hull:1964:MCR, author = "T. E. Hull and A. R. Dobell", title = "Mixed Congruential Random Number Generators for Binary Machines", journal = j-J-ACM, volume = "11", number = "1", pages = "31--40", month = jan, year = "1964", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321203.321208", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Thu Nov 03 22:33:52 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "Random number generators of the mixed congruential type have recently been proposed. They appear to have some advantages over those of the multiplicative type, except that their statistical behavior is unsatisfactory in some cases. It is shown theoretically that a certain class of these mixed generators should be expected to fail statistical tests for randomness. Extensive testing confirms this hypothesis and makes possible a more precise definition of the unsatisfactory class. It is concluded that the advantages of mixed generators can be realized only in special circumstances. On machines with relatively short multiplication times the multiplicative generators are to be preferred.", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Jagerman:1964:AJD, author = "David L. Jagerman", title = "The Autocorrelation and Joint Distribution Functions of the Sequences $ \bigg \{ \frac {a}{m}j^2 \bigg \}, \bigg \{ \frac {a}{m}(j + \tau)^2 \bigg \} $", journal = j-MATH-COMPUT, volume = "18", number = "86", pages = "211--232", month = apr, year = "1964", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Jansson:1964:ABP, author = "Birger Jansson", title = "Autocorrelations between Pseudo-Random Numbers", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "4", number = "1", pages = "6--27", month = mar, year = "1964", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01939521", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Wed Jan 4 18:52:08 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=4&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=1&spage=6", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/10543", } @Article{Jansson:1964:GRB, author = "Birger Jansson", title = "Generation of Random Bivariate Normal Deviates and Computation of Related Integrals", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "4", number = "4", pages = "205--212", month = dec, year = "1964", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01939512", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Wed Jan 4 18:52:08 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=4&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=4&spage=205", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/10543", } @Article{Johnk:1964:EBG, author = "M. D. J{\"o}hnk", title = "{Erzeugung von betaverteilten und gammaverteilten Zufallszahlen}. ({German}) [{Production} of beta- and gamma-distributed random numbers]", journal = j-METRIKA, volume = "8", number = "1", pages = "5--15", month = dec, year = "1964", CODEN = "MTRKA8", DOI = "https://doi.org/10.1007/BF02613706", ISSN = "0026-1335 (print), 1435-926X (electronic)", ISSN-L = "0026-1335", bibdate = "Mon Feb 2 16:27:32 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/metrika.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://link.springer.com/article/10.1007/BF02613706", ZMnumber = "0117.13203", acknowledgement = ack-nhfb, fjournal = "Metrika", journal-URL = "http://link.springer.com/journal/184", keywords = "{probability theory}", language = "German", } @Article{Kronmal:1964:EPN, author = "Richard Kronmal", title = "Evaluation of a Pseudorandom Normal Number Generator", journal = j-J-ACM, volume = "11", number = "3", pages = "357--363", month = jul, year = "1964", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321229.321238", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Tue Nov 1 00:45:35 1994", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, descriptors = "RVG", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @InProceedings{Liu:1964:MFS, author = "R. Liu and J. Massey", editor = "????", booktitle = "Proceedings of the 2nd Allerton Conference on Circuit and System Theory. University of Illinois, Urbana, 1964", title = "Monotone feedback shift registers", publisher = "????", address = "????", pages = "860--874", year = "1964", LCCN = "????", bibdate = "Tue Feb 07 11:12:28 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{MacLaren:1964:FPG, author = "M. D. MacLaren and G. Marsaglia and T. A. Bray", title = "A fast procedure for generating exponential random variables", journal = j-CACM, volume = "7", number = "5", pages = "298--300", month = may, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:53 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0127.09101", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7614", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "numerical analysis; PRNG (pseudo-random number generator)", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Marsaglia:1964:CMG, author = "G. Marsaglia and T. A. Bray", title = "A Convenient Method for Generating Normal Variables", journal = j-SIAM-REVIEW, volume = "6", number = "3", pages = "260--264", month = "????", year = "1964", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1006063", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65.15", MRnumber = "30 \#2660", MRreviewer = "D. H. Lehmer", bibdate = "Thu Mar 27 09:05:15 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/6/3; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib; MathSciNet database", URL = "http://www.jstor.org/stable/2027592", ZMnumber = "0125.08001", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", keywords = "numerical analysis", onlinedate = "July 1964", } @Article{Marsaglia:1964:FPG, author = "G. Marsaglia and M. D. MacLaren and T. A. Bray", title = "A fast procedure for generating normal random variables", journal = j-CACM, volume = "7", number = "1", pages = "4--10", month = jan, year = "1964", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/363872.363883", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:51 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib; http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0127.09005", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7637", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "numerical analysis; PRNG (pseudo-random number generator)", location = "SEL: Wi", references = "0", revision = "16/01/94", } @TechReport{Marsaglia:1964:MPR, author = "George Marsaglia", title = "A Method for Producing Random Variables in a Computer", type = "Mathematical note", number = "342", institution = "Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", pages = "13", month = feb, year = "1964", bibdate = "Tue Jun 21 18:14:31 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "This paper describes a general procedure for producing random variables in a computer. The idea is to represent the required $X$ in the form: $ X = C (M + U_1 + U_2 + U_3) $, some 97--99\% of the time, where c is constant, $M$ is a discrete random variable taking perhaps $8$ values, and the $U$'s are uniform random variables; the other 1--3\% of the time, $X$ is generated from a residual density by the rejection technique. These two methods for producing $X$ are combined in the proper proportions in order that the resulting distribution for $X$ be correct. The method is general in that it applies to a wide variety of density functions. Programs based on this procedure are very fast and require little computer storage space --- typically, 18 constants and 20 instructions.", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1964:RDA, author = "George Marsaglia", title = "The Radiation Dose Accumulated by Blood Diverted Through a Shunt", type = "Mathematical note", number = "357", institution = "Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", pages = "8", month = jul, year = "1964", bibdate = "Tue Jun 21 19:32:04 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "Modern techniques have made it possible to divert a portion of the circulating blood through a shunt outside the body --- for example in heart-lung machines, artificial kidneys, and coiled tubes where the blood may be exposed to radiation without danger to body tissues. There is some probability theory connected with such procedures, for the cells of the blood are thoroughly mixed in the body, and hence the number of times a blood cell passes through the shunt is a random variable. Several papers have been written to describe such systems by differential equations; this paper discusses the problem directly in terms of probability theory, finding the exact distribution of the number of times a blood cell has passed through the shunt and, in addition, a normal approximation which makes calculation of accumulated doses a matter of simple arithmetic.", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1964:RNV, author = "George Marsaglia", title = "Ratios of normal variables and ratios of sums of variables", type = "Mathematical note", number = "D1-82-0348", institution = "Mathematics Research Laboratory, Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", pages = "iii + 13 + 3", month = apr, year = "1964", bibdate = "Wed Nov 12 07:14:08 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0600972; http://www.dtic.mil/dtic/tr/fulltext/u2/600972.pdf; http://www.dtic.mil/get-tr-doc/pdf?AD=AD0600972", abstract = "The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the bivariate normal distribution and Nicholson's $V$ function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal.\par The last part of the paper discusses the distribution of the ratio $ (u_1 + \cdots + u_n) / (v_1 + \cdots + v_m)$ where the $u$'s and $v$'s are, independent, uniform variables. The distribution for all $n$ and $m$ is given, and some approximations discussed.", acknowledgement = ack-nhfb, remark = "Published in \cite{Marsaglia:1965:RNV}.", } @InCollection{Marsaglia:1964:RVC, author = "George Marsaglia", title = "Random variables and computers", crossref = "Kozesnik:1964:TTP", pages = "499--512", year = "1964", MRclass = "65.05 (65.15)", MRnumber = "29 \#1721", bibdate = "Fri Jan 6 09:58:36 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", ZMnumber = "0123.36205", acknowledgement = ack-nhfb, keywords = "probability theory", } @TechReport{Marsaglia:1964:SPIa, author = "George Marsaglia", title = "Some Problems Involving Circular and Spherical Targets", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "19", month = apr, year = "1964", bibdate = "Wed Nov 12 07:42:28 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0600566", abstract = "This article is concerned with some problems which occur in certain tactical considerations: how should one place $k$ circles (spheres) in the plane (3-space) so that their union has the greatest standard normal probability measure, that is, so as to maximize the probability that a random normal point will fall in one or more of the circles (spheres). For $ k > 3$ the problem seems hopeless, (except for certain special situations); the case for $ k = 3$ is still unresolved and is being worked on by a number of investigators, and the case for $ k = 2$ is solved completely in this paper. The results for $ k = 2$ have some practical value when applied to actual problems arising in tactical considerations, and some theoretical value, as a method of attacking the problem for $ k > 3$.", acknowledgement = ack-nhfb, } @Article{Marsaglia:1964:SPIb, author = "George Marsaglia", title = "Some Problems Involving Circular and Spherical Targets", journal = j-OPER-RES, volume = "13", number = "1", pages = "18--27", month = jan # "\slash " # feb, year = "1964", CODEN = "OPREAI", DOI = "https://doi.org/10.1287/opre.13.1.18", ISSN = "0030-364X (print), 1526-5463 (electronic)", ISSN-L = "0030-364X", bibdate = "Tue Jun 21 18:50:19 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/167951", abstract = "This article is concerned with some problems that occur in certain tactical considerations: how should one place $k$ circles [spheres] in the plane [3-space] so that their union has the greatest standard normal probability measure, that is, so as to maximize the probability that a random normal point will fall in one or more of the circles [spheres]. For $ k > 3 $ the problem seems hopeless, (except for certain special situations); the case for $ k = 3 $ is still unresolved and is being worked on by a number of investigators, and the case for $ k = 2 $ is solved completely in this paper. The results for $ k = 2 $ have some practical value when applied to actual problems arising in tactical considerations, and some theoretical value, as a method of attacking the problem for $ k \geq 3 $.", acknowledgement = ack-nhfb, fjournal = "Operations Research", journal-URL = "http://pubsonline.informs.org/loi/opre", } @Book{Onicescu:1964:NSA, author = "O. Onicescu", title = "Nombres et syst{\`e}mes al{\'e}atoires. ({French}) [Random numbers and systems]", publisher = "{\'E}ditions Eyrolles", address = "Paris, France", pages = "280", year = "1964", LCCN = "????", MRnumber = "MR 172314", bibdate = "Thu Jan 19 07:59:22 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "Zbl 0105.11404", acknowledgement = ack-nhfb, language = "French", } @Book{Poore:1964:CPG, author = "Jesse H. Poore", title = "Computational procedures for generating and testing random numbers", publisher = "Division of Business and Economic Research, School of Business Administration, Louisiana Polytechnic Institute", address = "Ruston, UK", pages = "36", year = "1964", LCCN = "QA273 .P78", bibdate = "Tue Apr 29 20:39:05 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/probstat1960.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Probabilities", } @Article{Sobol:1964:PPR, author = "I. M. Sobol'", title = "Periods of pseudo-random sequences", journal = "Teor. Verojatnost. i Primenen.", volume = "9", pages = "367--373", year = "1964", CODEN = "????", ISSN = "0040-361X", MRclass = "60.99 (65.15)", MRnumber = "0163334 (29 \#637)", MRreviewer = "G. E. Noether", bibdate = "Thu Jan 19 08:19:38 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Akademija Nauk SSSR. Teorija Verojatnoste{\u\i} i ee Primenenija", } @Article{Stockmal:1964:CPR, author = "Frank Stockmal", title = "Calculations with Pseudo-Random Numbers", journal = j-J-ACM, volume = "11", number = "1", pages = "41--52", month = jan, year = "1964", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321203.321209", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Thu Nov 03 22:33:52 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Book{Tocher:1964:AS, author = "K. D. Tocher", title = "The Art of Simulation", publisher = "Van Nostrand", address = "Princeton, NJ, USA", pages = "viii + 184", year = "1964", LCCN = "TA177 .T6", bibdate = "Tue Jun 19 05:33:49 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Simulation methods", tableofcontents = "1. Introduction \\ 2. Sampling from a distribution \\ 3. More sampling methods \\ 4. Random number tables \\ 5. Random number generators \\ 6. Pseudo-random numbers \\ 7. Elementary sampling experiments \\ 8. Flow diagrams \\ 9. Estimation \\ 10. Simple queuing problems \\ 11. Further queue problems \\ 12. General simulation problems \\ 13. Design of simulation experiments", } @Article{Barker:1965:MCC, author = "A. A. Barker", title = "{Monte Carlo} Calculations of the Radial Distribution Functions for a Proton-Electron Plasma", journal = j-AUSTRALIAN-J-PHYS, volume = "18", number = "??", pages = "119--133", month = "????", year = "1965", CODEN = "AUJPAS", ISSN = "0004-9506 (print), 1446-5582 (electronic)", ISSN-L = "0004-9506", bibdate = "Tue Feb 07 12:05:40 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Australian Journal of Physics", remark = "See \cite[page 255, column 2]{Hitchcock:2003:HMH} and \cite{Peskun:1973:OMC} for the relation of this work to \cite{Metropolis:1953:ESC}.", } @Book{Barnett:1965:RNE, author = "Vic D. Barnett", title = "Random negative exponential deviates; 2 pair-wise correlated sets of 10,000 observations: with facilities for the generation of random $ \chi^2 $ deviates on any integral number of degrees of freedom", volume = "27", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xxii + 89", year = "1965", LCCN = "QA47 .T7 no. 27", bibdate = "Mon Jun 27 13:35:14 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "Tracts for computers", acknowledgement = ack-nhfb, subject = "Sampling (Statistics); Stochastic processes", } @Article{Franklin:1965:NSS, author = "Joel N. Franklin", title = "Numerical Simulation of Stationary and Non-Stationary {Gaussian} Random Processes", journal = j-SIAM-REVIEW, volume = "7", number = "1", pages = "68--80", month = "????", year = "1965", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1007007", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRnumber = "MR 179913", bibdate = "Thu Mar 27 09:05:20 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/7/1; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1965", } @Book{Golenko:1965:MSA, author = "D. I. Golenko", title = "Modelirovanie i statisticheskii analiz psevdosluchainykh chisel na elektronnykh vychislitelnykh mashinakh. ({Russian}) [{The} method of statistical testing (The {Monte Carlo} method)]", publisher = "Izdatelstvo ``Nauka''", address = "Moscow, USSR", pages = "227", year = "1965", LCCN = "????", MRclass = "65.15 (10.03)", MRnumber = "0187370 (32 \#4822)", MRreviewer = "D. H. Lehmer", bibdate = "Wed Jan 18 18:08:00 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Russian", } @Article{Greenberger:1965:MR, author = "Martin Greenberger", title = "Method in randomness", journal = j-CACM, volume = "8", number = "3", pages = "177--179", month = mar, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:19:59 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "Certain nonrandom properties of a commonly used random number generator are described and analyzed.", acknowledgement = ack-nhfb, checked = "19940404", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "CDC 1604; floating-point arithmetic; PRNG (pseudo-random number generator); triple-precision floating-point arithmetic", sjb = "Points out that random number generators aren't always particularly random and that you should test the randomness properties of an algorithm yourself before using it in your code.", } @Article{Hampton:1965:EUP, author = "Robert L. Hampton", title = "Experiments Using Pseudo-Random Noise", journal = j-SIMULATION, volume = "4", number = "4", pages = "246--254", month = apr, year = "1965", CODEN = "SIMUA2", ISSN = "0037-5497 (print), 1741-3133 (electronic)", ISSN-L = "0037-5497", bibdate = "Wed Jan 11 12:00:50 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://sim.sagepub.com/content/4/4/246.abstract", abstract = "This paper describes the results of experiments per formed with pseudo-random noise sequences. It is shown that Gaussian noise can be easily produced from such sequences. It is also demonstrated that the sequences themselves have a binomial probability distribution.\par The correlation technique investigated, using pseudo-random noise, makes possible a continuous recording of a system's impulse response without the use of any sophisticated hardware. The impulse response obtained from the cross-correlation experiment can be approached from either the positive or negative direction, i.e., $ \tau $ can be made not only a time delay, but also a time advance. This enables one to observe the trailing end of a waveform before viewing its leading end. It also permits a quick experimental verification of the correlation property that $ R_{x, y}(\tau) = R_{y, r}( - \tau) $. Examples for a first- and second-order system are given.", acknowledgement = ack-nhfb, fjournal = "Simulation", journal-URL = "http://sim.sagepub.com/content/by/year", } @Article{Hampton:1965:HAD, author = "R. L. T. Hampton", title = "A Hybrid Analog-Digital Pseudo Random Noise Generator", journal = j-SIMULATION, volume = "4", number = "3", pages = "179--199", month = mar, year = "1965", CODEN = "SIMUA2", DOI = "https://doi.org/10.1177/003754976500400315", ISSN = "0037-5497 (print), 1741-3133 (electronic)", ISSN-L = "0037-5497", bibdate = "Wed Jan 11 12:11:36 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://sim.sagepub.com/content/4/3/179.full.pdf+html", acknowledgement = ack-nhfb, fjournal = "Simulation", journal-URL = "http://sim.sagepub.com/content/by/year", } @Article{Jagerman:1965:STC, author = "D. L. Jagerman", title = "Some Theorems Concerning Pseudo-Random Numbers", journal = j-MATH-COMPUT, volume = "19", number = "91", pages = "418--426", month = jul, year = "1965", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @InProceedings{Jansson:1965:ASP, author = "B. Jansson", editor = "????", booktitle = "Proceedings of the {IFIP} Congress", title = "Analytical studies of pseudorandom number generators of the congruential type", publisher = "????", address = "????", pages = "371--372", year = "1965", LCCN = "????", bibdate = "Mon Jan 16 22:24:59 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Knuth:1965:CRS, author = "Donald E. Knuth", title = "Construction of a random sequence", journal = j-NORDISK-TIDSKR-INFORM-BEHAND, volume = "5", number = "4", pages = "246--250", year = "1965", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", MRclass = "10.50 (10.33)", MRnumber = "33 #5599", MRreviewer = "J. H. Halton", bibdate = "Fri Mar 22 18:03:29 MST 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/10543", } @Article{MacLaren:1965:URN, author = "M. Donald MacLaren and George Marsaglia", title = "Uniform Random Number Generators", journal = j-J-ACM, volume = "12", number = "1", pages = "83--89", month = jan, year = "1965", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321250.321257", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", MRclass = "65.15", MRnumber = "30 \#687 (MR 170449)", bibdate = "Mon Jan 22 17:05:44 MST 2001", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", ZMnumber = "0143.40101", abstract = "This paper discusses the testing of methods for generating uniform random numbers in a computer---the commonly used multiplicative and mixed congruential generators as well as two new methods. Tests proposed here are more stringent than those usually applied, because the usual tests for randomness have passed several of the commonly-used procedures which subsequently gave poor results in actual Monte Carlo calculations. The principal difficulty seems to be that certain simple functions of $n$-tuples of uniform random numbers do not have the distribution that probability theory predicts.\par Two alternative generating methods are described, one of them using a table of uniform numbers, the other one combining two congruential generators. Both of these methods passed the tests, whereas the conventional multiplicative and mixed congruential methods did not.", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", keywords = "numerical analysis", oldlabel = "MacLarenM65", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/jacm/MacLarenM65", } @TechReport{Marsaglia:1965:SAM, author = "George Marsaglia", title = "Still Another Method for Producing Normal Variables in a Computer", type = "Mathematical note", number = "??", institution = "Boeing Scientific Research Laboratories", address = "Seattle, WA, USA", pages = "8", month = jan, year = "1965", bibdate = "Tue Jun 21 18:58:31 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A method for producing normal random variables in terms of uniform random variables $ U_1, U_2, U_3, \ldots {} $. If $ Y = U_1 + U_2 + U_3 $, then choosing one of the four random variables $ 2 Y - 3 $, $ (4 Y - 6) / 3 $, $ (Y - 7) / 2 $ or $ (Y + 4) / 2 $ in the proportions $ 0.8365 $, $ 0.11506 $, $ 0.00372 $ and $ 0.00372 $ will produce the required normal variate $ 98.6 $ per cent of the time. The other $ 1.4 $ per cent is devoted to the tail or a rejection technique in order that the composite be exact. The method leads to very fast computer programs which are easy to code and occupy little space in the computer.", acknowledgement = ack-nhfb, } @Book{Papoulis:1965:PRV, author = "Athanasios Papoulis", title = "Probability, random variables, and stochastic processes", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xi + 583", year = "1965", ISBN = "0-07-048448-1, 0-07-085971-X", ISBN-13 = "978-0-07-048448-1, 978-0-07-085971-5", LCCN = "QA273 .P2", bibdate = "Tue Jan 17 09:49:51 MST 2012", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, remark = "See other editions \cite{Papoulis:1984:PRV,Papoulis:1991:PRV,Papoulis:2002:PRV}.", } @Article{Pike:1965:AAP, author = "M. C. Pike and I. D. Hill", title = "{ACM Algorithm 266}: Pseudo-Random Numbers", journal = j-CACM, volume = "8", number = "10", pages = "605--606", month = oct, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Thu Sep 08 09:32:34 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See certification \cite{Sullins:1972:CAP}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Pike:1965:APR, author = "M. C. Pike and I. D. Hill", title = "{Algorithm 266}: {Pseudo}-random numbers [{G5}]", journal = j-CACM, volume = "8", number = "10", pages = "605--606", month = oct, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:02 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See certification \cite{Sullins:1972:CAP} and remarks \cite{Hansson:1966:RAG,Pike:1966:RAG}", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Pike:1965:ARN, author = "M. C. Pike", title = "{Algorithm 267}: {Random} normal deviate [{G5}]", journal = j-CACM, volume = "8", number = "10", pages = "606--606", month = oct, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:02 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Pike:1965:CAGb, author = "M. C. Pike", title = "Certification of {Algorithm 200} [{G5}]: {Normal} random", journal = j-CACM, volume = "8", number = "9", pages = "556--556", month = sep, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:02 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{George:1963:ANR}.", acknowledgement = ack-nhfb, checked = "19940408", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Potter:1965:CNS, author = "J. E. Potter", title = "Classroom Notes: Sets of {Gaussian} Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "72", number = "2", pages = "171--173", month = feb, year = "1965", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Thu Jul 8 18:23:41 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Pyke:1965:S, author = "R. Pyke", title = "Spacings", journal = j-J-R-STAT-SOC-SER-B-METHODOL, volume = "27", number = "??", pages = "395--434", month = "????", year = "1965", CODEN = "JSTBAJ", ISSN = "0035-9246", bibdate = "Wed Feb 08 19:09:43 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series B (Methodological)", journal-URL = "http://www.jstor.org/journals/00359246.html", } @Article{Reeves:1965:AUR, author = "C. M. Reeves", title = "Algorithm 8: a uniform random number generator", journal = j-COMPUT-BULL, volume = "9", number = "??", pages = "105--??", month = "????", year = "1965", CODEN = "COBUAH", ISSN = "0010-4531 (print), 1464-357X (electronic)", ISSN-L = "0010-4531", bibdate = "Mon Jan 16 22:27:29 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "The Computer Bulletin", } @Article{Rosenberg:1965:CNN, author = "Lloyd Rosenberg", title = "Classroom Notes: Nonnormality of Linear Combinations of Normally Distributed Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "72", number = "8", pages = "888--890", month = oct, year = "1965", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:00 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Scheinok:1965:DFR, author = "P. Scheinok", title = "The Distribution Functions of Random Variables in Arithmetic Domains Modulo $a$", journal = j-AMER-MATH-MONTHLY, volume = "72", number = "2", pages = "128--134", month = feb, year = "1965", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Thu Jul 8 18:23:41 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Seshadri:1965:RVW, author = "V. Seshadri", title = "On random variables which have the same distribution as their reciprocals", journal = j-CAN-MATH-BULL, volume = "8", number = "??", pages = "819--824", month = "????", year = "1965", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1965-062-7", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", bibdate = "Thu Sep 8 10:03:13 MDT 2011", bibsource = "http://cms.math.ca/cmb/v8/; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", } @Article{Shapiro:1965:DAA, author = "Jesse M. Shapiro", title = "Domains of Attraction for Absolute Values of Random Variables", journal = j-J-SIAM, volume = "13", number = "1", pages = "129--135", month = mar, year = "1965", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Journal of the Society for Industrial and Applied Mathematics", journal-URL = "http://epubs.siam.org/loi/smjmap.1", } @Article{Stoneham:1965:SDT, author = "R. G. Stoneham", title = "A study of the 60,000 digits of the transcendental `$e$'", journal = j-AMER-MATH-MONTHLY, volume = "72", number = "4", pages = "483--506", month = apr, year = "1965", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Sat Jan 07 11:35:50 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Tausworthe:1965:RNG, author = "Robert C. Tausworthe", title = "Random Numbers Generated by Linear Recurrence Modulo Two", journal = j-MATH-COMPUT, volume = "19", number = "90", pages = "201--209", month = apr, year = "1965", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.15", MRnumber = "32 \#1878", MRreviewer = "J. H. Halton", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "Distributed/QLD.bib; Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/2003345", acknowledgement = ack-nhfb, annote = "Many situations arise in various fields of interest for which the mathematical model utilizes a random sequence of numbers, events, or both. In many of these applications, it is often extremely advantageous to generate, by some deterministic means, a sequence which appears to be random, even if, upon closer and longer observations, certain regularities become evident. For example, electronic computer programs for generating random numbers to be \ldots{}", date = "09/06/82", descriptors = "Tausworthe generator; method; RNG; test; Shift register sequences", enum = "3054", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", location = "RWTH-AC-DFV: MB; PKI-OG: Li-Ord.Le", references = "8", revision = "21/04/91", } @Article{Teichroew:1965:HDS, author = "Daniel Teichroew", title = "A history of distribution sampling prior to the era of the computer and its relevance to simulation", journal = j-J-AM-STAT-ASSOC, volume = "60", number = "309", pages = "27--49", month = mar, year = "1965", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Jan 9 17:34:07 2012", bibsource = "Distributed/QLD.bib; Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2283135", acknowledgement = ack-nhfb, date = "13/05/93", descriptors = "RVG", enum = "7970", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", location = "SEL: Wi", revision = "16/01/94", } @Article{Chaitin:1966:LPC, author = "Gregory J. Chaitin", title = "On the Length of Programs for Computing Finite Binary Sequences", journal = j-J-ACM, volume = "13", number = "4", pages = "547--569", month = oct, year = "1966", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321356.321363", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Sat Jan 26 12:46:16 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "The use of Turing machines for calculating finite binary sequences is studied from the point of view of information theory and the theory of recursive functions. Various results are obtained concerning the number of:instructions ia programs. A modified form of Turing machine is studied from the same point of view. Aa application to the problem of defining a patternless sequence is proposed in terms of the concepts here developed.", acknowledgement = ack-ds # " and " # ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", rawdata = "Chaitin, Gregory J. (1966) ``On the Lengths of Programs for Computing Finite Binary Sequences,'' {\it Journal of the ACM}, {\bf13}(4):547--569, October.", } @Article{Chiang:1966:ERR, author = "C. L. Chiang", title = "On the Expectation of the Reciprocal of a Random Variable", journal = j-AMER-STAT, volume = "20", number = "4", pages = "28--28", month = oct, year = "1966", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:37 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326494; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2685960", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Dyadkin:1966:SRE, author = "I. G. Dyad'kin", title = "Simulation of the random energy of a gamma quantum scattered as a result of the {Compton} effect", journal = j-USSR-COMP-MATH-MATH-PHYS, volume = "6", number = "2", pages = "274--276", month = "????", year = "1966", CODEN = "CMMPA9", DOI = "https://doi.org/10.1016/0041-5553(66)90077-2", ISSN = "0041-5553, 0502-9902", ISSN-L = "0041-5553", bibdate = "Mon Feb 27 09:47:25 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "English translation of Russian original published in Zh. vychisl. Mat. mat. Fiz. {\bf 6}(2) 384--385, 1966.", URL = "http://www.sciencedirect.com/science/article/pii/0041555366900772", abstract = "When the Monte Carlo method is used to solve problems on the propagation of gamma quanta in a material, the greater part of the computer time is expended in simulating the Compton effect. An economic algorithm is proposed below for converting random numbers, uniformly distributed over the interval $ (0, 1) $, into the energy of the scattered gamma quantum.", acknowledgement = ack-nhfb, fjournal = "U.S.S.R. Computational Mathematics and Mathematical Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00415553", } @Article{Fleiss:1966:NER, author = "Joseph L. Fleiss", title = "A Note on the Expectation of the Reciprocal of a Random Variable", journal = j-AMER-STAT, volume = "20", number = "1", pages = "25--25", month = feb, year = "1966", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:37 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326344; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2681673", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Gorenstein:1966:APN, author = "S. Gorenstein", title = "Another pseudorandom number generator", journal = j-CACM, volume = "9", number = "9", pages = "711", month = sep, year = "1966", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 16 22:21:17 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", xxmonth = oct, xxnote = "Article missing from ACM Portal database; it is either at the end of issue 9 (most likely), or the start of issue 10 (unlikely).", xxnumber = "10", } @Article{Hansson:1966:RAG, author = "L. Hansson", title = "Remark on {Algorithm 266 [G5]}: Pseudo-Random Numbers", journal = j-CACM, volume = "9", number = "9", pages = "687--687", month = sep, year = "1966", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/365813.365839", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:09 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Pike:1965:APR}, remark \cite{Pike:1966:RAG}, and certification \cite{Sullins:1972:CAP}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Heyde:1966:SRS, author = "C. C. Heyde", title = "Some results on small-deviation probability convergence rates for sums of independent random variables", journal = j-CAN-J-MATH, volume = "18", number = "??", pages = "656--665", month = "????", year = "1966", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1966-066-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:35 MDT 2011", bibsource = "http://cms.math.ca/cjm/v18/; https://www.math.utah.edu/pub/tex/bib/canjmath1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hutchinson:1966:NUP, author = "David W. Hutchinson", title = "A new uniform pseudorandom number generator", journal = j-CACM, volume = "9", number = "6", pages = "432--433", month = jun, year = "1966", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.15", MRnumber = "33\#1954", bibdate = "Tue May 28 07:34:50 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A new multiplicative congruential pseudorandom number generator is discussed, in which the modulus is the largest prime within accumulator capacity and the multiplier is a primitive root of that prime. This generator passes the usual statistical tests and in addition the least significant bits appear to be as random as the most significant bits-a property which generators having modulus $ 2^k $ do not possess.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Book{Jansson:1966:RNG, author = "Birger Jansson", title = "Random number generators", publisher = "Almqvist \& Wiksell", address = "Stockholm, Sweden", pages = "205", year = "1966", LCCN = "QA276.5 .J3 1966", MRnumber = "MR 224253", bibdate = "Wed Dec 21 10:20:08 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, } @Article{Loveland:1966:NIM, author = "D. Loveland", title = "A New Interpretation of the {von Mises} Concept of Random Sequence", journal = j-Z-MATH-LOGIK-GRUNDL-MATH, volume = "12", number = "??", pages = "279--294", month = "????", year = "1966", CODEN = "ZMLGAQ", ISSN = "0044-3050", bibdate = "Mon Feb 20 15:33:13 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r mathematische Logik und Grundlagen der Mathematik}", } @InProceedings{Marsaglia:1966:GMP, author = "G. Marsaglia", booktitle = "Proceedings of the Fall Joint Computer Conference, San Francisco, November 1966", title = "A general method for producing random variables in a computer", publisher = "Spartan Books", address = "Washington, DC, USA", bookpages = "vii + 819", pages = "169--173", year = "1966", LCCN = "TK7885.A1 J74 1966 Fall", bibdate = "Fri Jan 6 09:58:50 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7631", location = "SEL: Wi", references = "0", revision = "16/01/94", town = "San Francisco", } @Article{Martin-Lof:1966:CRS, author = "P. Martin-L{\"o}f", title = "On the Concept of a Random Sequence", journal = j-THEORY-PROBAB-APPL, volume = "11", number = "??", pages = "177--179", month = "????", year = "1966", CODEN = "TPRBAU", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Mon Feb 20 15:41:26 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", } @Article{Martin-Lof:1966:DRS, author = "Per Martin-L{\"o}f", title = "The definition of random sequences", journal = j-INF-CONTROL, volume = "9", number = "6", pages = "602--619", month = dec, year = "1966", CODEN = "IFCNA4", DOI = "https://doi.org/10.1016/S0019-9958(66)80018-9", ISSN = "0019-9958 (print), 1878-2981 (electronic)", ISSN-L = "0019-9958", bibdate = "Mon Jan 16 22:23:52 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Information and Control", journal-URL = "http://www.sciencedirect.com/science/journal/00199958", } @Article{Mckinney:1966:CNG, author = "E. H. Mckinney", title = "Classroom Notes: Generalized Birthday Problem", journal = j-AMER-MATH-MONTHLY, volume = "73", number = "4", pages = "385--387", month = apr, year = "1966", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Fri Jul 9 10:43:31 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Miller:1966:BRB, author = "Irwin Miller", title = "Book Review: {{\booktitle{Probability, Random Variables, and Stochastic Processes}} by Anthanasios Papoulis}", journal = j-TECHNOMETRICS, volume = "8", number = "2", pages = "378--380", month = may, year = "1966", CODEN = "TCMTA2", DOI = "https://doi.org/10.2307/1266379", ISSN = "0040-1706 (print), 1537-2723 (electronic)", ISSN-L = "0040-1706", bibdate = "Sat Jun 21 13:17:51 MDT 2014", bibsource = "http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254246; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib", URL = "http://www.jstor.org/stable/1266379", acknowledgement = ack-nhfb, fjournal = "Technometrics", journal-URL = "http://www.jstor.org/journals/00401706.html", } @Article{Murthy:1966:NER, author = "V. N. Murthy and C. S. Pillai", title = "A Note on the Expectation of the Reciprocal and Square Root of a Random Variable", journal = j-AMER-STAT, volume = "20", number = "5", pages = "30--30", month = dec, year = "1966", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:37 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326347; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682640", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Pike:1966:RAG, author = "M. C. Pike and I. D. Hill", title = "Remark on {Algorithm 266 [G5]}: Pseudo-Random Numbers", journal = j-CACM, volume = "9", number = "9", pages = "687--687", month = sep, year = "1966", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/365813.365839", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:09 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Pike:1965:APR}, remark \cite{Hansson:1966:RAG}, and certification \cite{Sullins:1972:CAP}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Book{RAND:1966:MRD, author = "{RAND Corporation}", title = "A Million Random Digits With 100,000 Normal Deviates", publisher = pub-FREE, address = pub-FREE:adr, pages = "xxviii + 400 + 200", year = "1966", LCCN = "QA276.5 .R3", bibdate = "Sat Aug 23 07:58:03 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Reprint of original edition \cite{RAND:1955:MRD}. Reprinted in 2001 \cite{RAND:2001:MRD}. See also \cite{Tippett:1927:RSN,Brown:1949:HRR,Brown:1951:HRR}.", URL = "http://www.rand.org/pubs/monograph_reports/MR1418.html", acknowledgement = ack-nhfb, HDnumber = "100", } @Book{Shreider:1966:MCM, editor = "I. A. (Ulii Anatol'evich) Shreider and N. P. (Nikolai Panteleimonovich) Buslenko", title = "The {Monte Carlo} method; the method of statistical trials", volume = "87", publisher = pub-PERGAMON, address = pub-PERGAMON:adr, pages = "xii + 381", year = "1966", LCCN = "QA273 .S5611", bibdate = "Sat Jan 7 12:03:03 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; library.mit.edu:9909/mit01", series = "International series of monographs in pure and applied mathematics", acknowledgement = ack-nhfb, remark = "Translation of Russian original \booktitle{Metod statisticheskikh ispytanii; metod Monte-Karlo}.", subject = "Monte Carlo method", } @Article{Spitzer:1966:RPP, author = "Frank Spitzer", title = "Recent Publications and Presentations: {{\em Information and Information Stability of Random Variables and Processes}}, by {M. S. Pinsker}", journal = j-AMER-MATH-MONTHLY, volume = "73", number = "8", pages = "912--913", month = oct, year = "1966", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:23 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Springer:1966:DPI, author = "M. D. Springer and W. E. Thompson", title = "The Distribution of Products of Independent Random Variables", journal = j-SIAM-J-APPL-MATH, volume = "14", number = "3", pages = "511--526", month = may, year = "1966", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Book{Stroud:1966:GQF, author = "A. H. Stroud and Don Secrest", title = "{Gaussian} Quadrature Formulas", publisher = pub-PH, address = pub-PH:adr, pages = "ix + 374", year = "1966", LCCN = "QA299.4.G3 S7 1966", bibdate = "Sun Jan 17 09:52:34 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, remark = "See also \cite{Stroud:1971:ACM}.", xxISBN = "none", } @Article{Zaremba:1966:GLP, author = "S. C. Zaremba", title = "Good lattice points, discrepancy, and numerical integration", journal = j-ANN-MAT-PURA-APPL-4, volume = "73", number = "??", pages = "293--317", month = "????", year = "1966", CODEN = "ANLMAE", ISSN = "0003-4622", MRclass = "65.55", MRnumber = "0218018 (36 \#1107)", MRreviewer = "S. Haber", bibdate = "Thu Jan 19 08:32:45 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Annali di matematica pura ed applicata. Series 4", } @Article{Albert:1967:CNN, author = "G. E. Albert and R. L. Tittle", title = "Classroom Notes: Nonnormality of Linear Combinations of Normally Distributed Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "74", number = "5", pages = "583--585", month = may, year = "1967", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:39 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Azorin:1967:BRB, author = "F. Azor{\'\i}n", title = "Book Review: {{\booktitle{Random Number Generators}}, by B. Jansson}", journal = j-REV-INST-INT-STATIST, volume = "35", number = "1", pages = "95--96", month = "????", year = "1967", CODEN = "????", ISSN = "0373-1138", bibdate = "Wed Dec 21 10:21:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Jansson:1966:RNG}.", URL = "http://www.jstor.org/stable/1401645", acknowledgement = ack-nhfb, fjournal = "Revue de l'Institut international de statistique = Review of the International Statistical Institute", } @Article{Behboodian:1967:EAV, author = "Javad Behboodian", title = "On the Expectation of the Absolute Value of a Random Vector", journal = j-AMER-STAT, volume = "21", number = "4", pages = "25--26", month = oct, year = "1967", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326351; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682101", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @InProceedings{Canavos:1967:CAT, author = "G. C. Canavos", editor = "????", booktitle = "{Proceedings of the 22nd Conference of the ACM}", title = "A comparative analysis of two concepts in the generation of uniform pseudorandom numbers", publisher = pub-ACM, address = pub-ACM:adr, pages = "485--501", year = "1967", LCCN = "????", bibdate = "Mon Jan 16 22:16:18 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Chambers:1967:RNG, author = "R. P. Chambers", title = "Random-number generation on digital computers", journal = j-IEEE-SPECTRUM, volume = "4", number = "2", pages = "48--56", month = feb, year = "1967", CODEN = "IEESAM", DOI = "https://doi.org/10.1109/MSPEC.1967.5216203", ISSN = "0018-9235 (print), 1939-9340 (electronic)", ISSN-L = "0018-9235", bibdate = "Wed Jan 15 09:12:12 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Spectrum", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6", keywords = "Application software; Arithmetic; Debugging; Game theory; Inductors; Laboratories; Mesh generation; Military computing; Probability; Sampling methods", } @Article{Coveyou:1967:FAU, author = "R. R. Coveyou and R. D. MacPherson", title = "{Fourier} Analysis of Uniform Random Number Generators", journal = j-J-ACM, volume = "14", number = "1", pages = "100--119", month = jan, year = "1967", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321371.321379", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Thu Dec 22 07:42:22 2011", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A method of analysis of uniform random number generators is developed, applicable to almost all practical methods of generation. The method is that of Fourier analysis of the output sequences of such generators. With this tool it is possible to understand and predict relevant statistical properties of such generators and compare and evaluate such methods. Many such analyses and comparisons have been carried out. The performance of these methods as implemented on differing computers is also studied. The main practical conclusions of the study are: (a) Such a priori analysis and prediction of statistical behavior of uniform random number generators is feasible. (b) The commonly used multiplicative congruence method of generation is satisfactory with careful choice of the multiplier for computers with an adequate ($ \geq \tilde $ 35-bit) word length. (c) Further work may be necessary on generators to be used on machines of shorter word length.", acknowledgement = ack-nhfb, descriptors = "Shift register sequences; method; spectral analysis; interdependence; multidimensional uniformity; RNG; test", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", remark = "This article is believed to be the origin of the spectral test for randomness.", } @Article{Csorgo:1967:NPS, author = "Mikl{\'o}s Cs{\"o}rg{\"o}", title = "A new proof of some results of {R{\'e}nyi} and the asymptotic distribution of the range of his {Kolmogorov--Smirnov} type random variables", journal = j-CAN-J-MATH, volume = "19", number = "??", pages = "550--558", month = "????", year = "1967", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1967-048-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:36 MDT 2011", bibsource = "http://cms.math.ca/cjm/v19/; https://www.math.utah.edu/pub/tex/bib/canjmath1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{deBalbine:1967:NRP, author = "Guy {de Balbine}", title = "Note on Random Permutations (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "21", number = "100", pages = "710--712", month = oct, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Downham:1967:MCP, author = "D. Y. Downham and F. D. K. Roberts", title = "Multiplicative congruential pseudo-random number generators", journal = j-COMP-J, volume = "10", number = "1", pages = "74--77", month = may, year = "1967", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:51:17 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/compj1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/100074.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/74.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/75.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/76.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/77.tif", acknowledgement = ack-nhfb, fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", } @Article{Gabai:1967:DCS, author = "H. Gabai", title = "On the discrepancy of certain sequences $ \bmod 1 $", journal = j-ILL-J-MATH, volume = "11", number = "??", pages = "1--12", month = "????", year = "1967", CODEN = "IJMTAW", ISSN = "0019-2082 (print), 1945-6581 (electronic)", ISSN-L = "0019-2082", bibdate = "Thu Jan 19 06:48:35 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Illinois Journal of Mathematics", } @Article{Gebhardt:1967:GPR, author = "Friedrich Gebhardt", title = "Generating Pseudo-Random Numbers by Shuffling a {Fibonacci} Sequence (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "21", number = "100", pages = "708--709", month = oct, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gebhardt-friedrich.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Book{Golomb:1967:SRS, author = "Solomon W. (Solomon Wolf) Golomb", title = "Shift Register Sequences", publisher = pub-HOLDEN-DAY, address = pub-HOLDEN-DAY:adr, pages = "xiv + 224", year = "1967", LCCN = "QA267.5.S4 G6", bibdate = "Sat Sep 17 13:57:12 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", note = "Portions co-authored by Lloyd R. Welch, Richard M. Goldstein and Alfred W. Hales.", series = "Holden-Day series in information systems", acknowledgement = ack-nhfb, subject = "Coding theory; Switching theory; Sequential machine theory; Shift registers", } @Article{Good:1967:GST, author = "I. J. Good and T. N. Gover", title = "The generalized serial test and the binary expansion of $ \sqrt {2} $", journal = j-J-R-STAT-SOC-SER-A-GENERAL, volume = "130", number = "1", pages = "102--107", month = "????", year = "1967", CODEN = "JSSAEF", ISSN = "0035-9238", bibdate = "Sat Jan 07 11:23:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See remark \cite{Good:1968:GST}.", URL = "http://www.jstor.org/stable/2344040", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series A (General)", journal-URL = "http://www.jstor.org/journals/00359238.html", remark = "The first author reports in \cite[page 43, column 2]{Good:1969:HRR}: ``For binary sequences one of the best tests is the generalized serial test. This test, which uses a statistic having the appearance of a `Chi-squared', is also useful when $ t \neq 2 $, but it does not have asymptotically a chi-squared distribution, a fact that has led to error in at least five published papers \cite{Forsythe:1951:GTRa,Kendall:1938:RRS,Pathria:1962:SSR,RAND:1955:MRD,Stoneham:1965:SDT}. It would have led to the rejection of RAND's million random digits if the test had been applied to many blocks incorrectly, instead of to only a few. The simple correct method of use is described in \cite{Good:1967:GST} [this paper].''", } @Article{Gorenstein:1967:TRN, author = "Samuel Gorenstein", title = "Testing a random number generator", journal = j-CACM, volume = "10", number = "2", pages = "111--118", month = feb, year = "1967", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:11 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Gurland:1967:ISE, author = "John Gurland", title = "An Inequality Satisfied by the Expectation of the Reciprocal of a Random Variable", journal = j-AMER-STAT, volume = "21", number = "2", pages = "24--25", month = apr, year = "1967", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326349; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682610", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Book{Hemmerle:1967:SCD, author = "William J. Hemmerle", title = "Statistical Computations on a Digital Computer", publisher = "Blaisdell", address = "Waltham, MA, USA", pages = "x + 230", year = "1967", LCCN = "QA276 .H42", bibdate = "Mon Jan 16 22:18:47 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @InProceedings{Itzelsberger:1967:SEP, author = "G. Itzelsberger", title = "Some experiences with the poker test for investigating pseudorandom numbers", crossref = "Hollingdale:1967:DSO", pages = "64--68", year = "1967", bibdate = "Mon Jan 16 22:19:25 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Marlow:1967:NLT, author = "N. A. Marlow", title = "A normal limit theorem for power sums of independent random variables", journal = j-BELL-SYST-TECH-J, volume = "46", number = "9", pages = "2081--2089", month = nov, year = "1967", CODEN = "BSTJAN", ISSN = "0005-8580", MRclass = "60.30", MRnumber = "0224135 (36 \#7181)", MRreviewer = "S. M. Samuels", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4609.html; http://www.alcatel-lucent.com/bstj/vol46-1967/bstj-vol46-issue09.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-9-2081.pdf; http://www.alcatel-lucent.com/bstj/vol46-1967/articles/bstj46-9-2081.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Mullen:1967:NRT, author = "Kenneth Mullen", title = "A Note on the Ratio of Two Independent Random Variables", journal = j-AMER-STAT, volume = "21", number = "3", pages = "30--31", month = jun, year = "1967", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326350; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682042", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Nasell:1967:SPP, author = "Ingemar Nasell", title = "Some Properties of Power Sums of Truncated Normal Random Variables", journal = j-BELL-SYST-TECH-J, volume = "46", number = "9", pages = "2091--2110", month = nov, year = "1967", CODEN = "BSTJAN", ISSN = "0005-8580", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4609.html; http://www.alcatel-lucent.com/bstj/vol46-1967/bstj-vol46-issue09.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-9-2091.pdf; http://www.alcatel-lucent.com/bstj/vol46-1967/articles/bstj46-9-2091.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @InProceedings{Page:1967:GPR, author = "E. S. Page", title = "The generation of pseudo-random numbers", crossref = "Hollingdale:1967:DSO", pages = "55--63", year = "1967", bibdate = "Thu Dec 22 10:01:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Ratz:1967:MPN, author = "Herbert C. Ratz and J. V. Hildebrand", title = "Modified Pseudorandom Number Generators", journal = j-IEEE-TRANS-ELEC-COMPUT, volume = "EC-16", number = "6", pages = "854--856", month = dec, year = "1967", CODEN = "IEECA8", DOI = "https://doi.org/10.1109/PGEC.1967.264749", ISSN = "0367-7508", bibdate = "Wed Jul 13 21:15:06 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039202", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electronic Computers", } @Article{Sclove:1967:FRE, author = "Stanley L. Sclove and Gordon Simons and J. {Van Ryzin}", title = "Further Remarks on the Expectation of the Reciprocal of a Positive Random Variable", journal = j-AMER-STAT, volume = "21", number = "4", pages = "33--34", month = oct, year = "1967", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326351; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682105", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Serfling:1967:NCR, author = "R. J. Serfling", title = "A Note on the Covariance of a Random Variable and Its Reciprocal", journal = j-AMER-STAT, volume = "21", number = "4", pages = "33--33", month = oct, year = "1967", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326351; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682104", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Sobol:1967:DPC, author = "I. M. Sobol'", title = "On the distribution of points in a cube and the approximate evaluation of integrals", journal = j-USSR-COMP-MATH-MATH-PHYS, volume = "7", number = "4", pages = "86--112", month = "????", year = "1967", CODEN = "CMMPA9", DOI = "https://doi.org/10.1016/0041-5553(67)90144-9", ISSN = "0041-5553, 0502-9902", ISSN-L = "0041-5553", bibdate = "Mon Feb 27 17:01:27 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "English translation of Russian original published in Zh. vychisl. Mat. mat. Fiz. {\bf 7}(4), 784--802, 1967.", URL = "http://www.sciencedirect.com/science/article/pii/0041555367901449", acknowledgement = ack-nhfb, fjournal = "U.S.S.R. Computational Mathematics and Mathematical Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00415553", } @InProceedings{Solomon:1967:RPD, author = "H. Solomon", editor = "Lucien M. {Le Cam} and Jerzy Neyman", booktitle = "{Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. Volume III. Physical Sciences}", title = "Random packing density", volume = "3", publisher = pub-U-CAL, address = pub-U-CAL:adr, pages = "119--134", year = "1967", LCCN = "QA276 .B4 v.3", bibdate = "Wed Feb 29 21:12:50 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/kepler.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Held at the Statistical Laboratory, University of California, June 21--July 18, 1965 and December 27, 1965--January 7, 1966.", URL = "http://projecteuclid.org/euclid.bsmsp/1200513624", acknowledgement = ack-nhfb, keywords = "parking-lot test; sphere packing", } @Article{Stein:1967:CPA, author = "Josef Stein", title = "Computational problems associated with {Racah} algebra", journal = j-J-COMPUT-PHYS, volume = "1", number = "3", pages = "397--405", month = feb, year = "1967", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(67)90047-2", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Sun Jan 1 08:27:59 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.sciencedirect.com/science/article/pii/0021999167900472", abstract = "In a program written by the author, for performing various calculations in the Racah algebra, some new calculational methods were used; these methods are described in this paper. They include: (1) a representation of numbers alternative to the Rotenberg form; (2) a new algorithm for calculating the greatest common divisor of two odd integers, which was developed for reducing the calculating time in the new representation; (3) methods for shortening the computation time of 3-j and 6-j symbols.", acknowledgement = ack-nhfb, affiliation = "The Hebrew University, Jerusalem, Israel", fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", keywords = "fast greatest common denominator (gcd)", remark = "This may be the earliest published paper about speeding up computation of the greatest common denominator (gcd). Brent \cite{Brent:2000:TYA} also cites earlier unpublished work of Silver and Terzian (1962), and quotes a translation of a first century AD Chinese text given by Knuth \cite[\S 4.5.2]{Knuth:1997:SA} that describes what we now call the ``binary Euclidean algorithm''.", } @Article{Strome:1967:AUR, author = "W. Murray Strome", title = "{Algorithm 294}: {Uniform} Random", journal = j-CACM, volume = "10", number = "1", pages = "40--40", month = jan, year = "1967", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:11 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "multiplicative congruential generator; PRNG (pseudo-random number generator)", remark = "User-provided $C$ and $M$ for $ x_{n + 1} = (C x_n) \bmod M $, but user must restrict parameter bit-widths to ensure representability of product done in floating-point arithmetic.", } @Article{VanGelder:1967:SNR, author = "A. {Van Gelder}", title = "Some New Results in Pseudo-Random Number Generation", journal = j-J-ACM, volume = "14", number = "4", pages = "785--792", month = oct, year = "1967", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321420.321437", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Tue Nov 1 09:50:45 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "Pseudo-random number generators of the power residue (sometimes called congruential or multiplicative) type are discussed and results of statistical tests performed on specific examples of this type are presented. Tests were patterned after the methods of MacLaren and Marsaglia (M\&M). The main result presented is the discovery of several power residue generators which performed well in these tests. This is important because, of all the generators using standard methods (including power residue) that were tested by M\&M, none gave satisfactory results. The overall results here provide further evidence for their conclusion that the types of tests usually encountered in the literature do not provide an adequate index of the behavior of n-tuples of consecutively generated numbers. In any Monte Carlo or simulation problem where n supposedly independent random numbers are required at each step, this behavior is likely to be important. Finally, since the tests presented here differ in certain details from those of M\&M, some of their generators were retested as a check. A cross-check shows that results are compatible; in particular, if a generator failed one of their tests badly, it also failed the present author's corresponding test badly.", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Westlake:1967:URN, author = "W. J. Westlake", title = "A Uniform Random Number Generator Based on the Combination of Two Congruential Generators", journal = j-J-ACM, volume = "14", number = "2", pages = "337--340", month = apr, year = "1967", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321386.321396", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Thu Dec 22 07:42:23 2011", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A method of generating pseudo-random uniform numbers based on the combination of two congruential generators is described. It retains two of the desirable features of congruential generators, namely, the long cycle and the case of implementation on a digital computer. Furthermore, unlike the method of combining congruential generators recently proposed by MacLaren and Marsaglia, it does not require the retention in computer memory of a table of generated numbers. The generator gave completely satisfactory results on a fairly stringent series of statistical tests.", acknowledgement = ack-nhfb, descriptors = "RNG", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{White:1967:EDC, author = "R. C. White", title = "Experiments with Digital Computer Simulations of Pseudo-Random Noise Generators", journal = j-IEEE-TRANS-ELEC-COMPUT, volume = "EC-16", number = "3", pages = "355--357", month = jun, year = "1967", CODEN = "IEECA8", DOI = "https://doi.org/10.1109/PGEC.1967.264694", ISSN = "0367-7508", bibdate = "Wed Jul 13 21:15:03 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039076", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electronic Computers", } @Article{Wyner:1967:RPC, author = "A. D. Wyner", title = "Random packings and coverings of the unit {$n$}-sphere", journal = j-BELL-SYST-TECH-J, volume = "46", number = "9", pages = "2111--2118", month = nov, year = "1967", CODEN = "BSTJAN", ISSN = "0005-8580", MRclass = "52.45 (60.00)", MRnumber = "0223979 (36 \#7026)", MRreviewer = "R. P. Bambah", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4609.html; http://www.alcatel-lucent.com/bstj/vol46-1967/bstj-vol46-issue09.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-9-2111.pdf; http://www.alcatel-lucent.com/bstj/vol46-1967/articles/bstj46-9-2111.pdf", abstract = "It is well known that the quantity $ M_p(n, 0) $, the maximum number of nonoverlapping spherical caps of half angle $ \theta $ (a ``packing'') which can be placed on the surface of a unit sphere in Euclidean $n$-space is not less than $ \exp [ - n \log \sin 2 \theta + o(n)] \quad (\theta < \pi / 4) $. In this paper we give a new proof of this fact by a ``random coding'' argument, the central part of which is a theorem which asserts that if a set of roughly $ \exp (n \log \sin 2 \theta) $ caps is chosen at random, that on the average only a very small fraction of the caps will overlap (when $n$ is large).\par A related problem is the determination of $ M_c(n, \theta) $, the minimum number of caps of half angle $ \theta $ required to cover the unit Euclidean $n$-sphere We show that $ M_c(n, \theta) = \exp [ - n \log \sin \theta + o(n)] $. The central part of the proof is also a random coding argument which asserts that if a set roughly $ \exp ( - n \log \sin \theta) $ caps is chosen at random, that on the average only a very small fraction of the surface of the $n$-sphere will remain uncovered (when $n$ is large).", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Adhikari:1968:DMS, author = "A. K. Adhikari and B. P. Sarkar", title = "Distribution of most significant digit in certain functions whose arguments are random variables", journal = j-SANKHYA-B, volume = "30", number = "??", pages = "47--58", month = "????", year = "1968", CODEN = "SANBBV", ISSN = "0581-5738", bibdate = "Sat Nov 12 16:09:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Sankhya Ser. B (Indian J. of Statist.)", fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B. Methodological", } @Article{Anonymous:1968:GCM, author = "Anonymous", title = "The generation of correlated multivariate samples for {Monte Carlo} simulation", journal = j-IEEE-SPECTRUM, volume = "5", number = "2", pages = "5--5", month = feb, year = "1968", CODEN = "IEESAM", DOI = "https://doi.org/10.1109/MSPEC.1968.5214753", ISSN = "0018-9235 (print), 1939-9340 (electronic)", ISSN-L = "0018-9235", bibdate = "Wed Jan 15 09:30:58 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Spectrum", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6", keywords = "Cellular neural networks; Covariance matrix; Delay lines; Filters; Gaussian processes; Information theory; Phased arrays; Signal generators; Signal processing; Stochastic processes", } @Article{Ayoub:1968:EEK, author = "F. Ayoub", title = "Erratum: Encryption with keyed random permutations", journal = j-ELECT-LETTERS, volume = "17", number = "??", pages = "??--??", month = feb, year = "1968", CODEN = "ELLEAK", DOI = "https://doi.org/10.1049/el:19810541", ISSN = "0013-5194 (print), 1350-911X (electronic)", ISSN-L = "0013-5194", bibdate = "Fri Dec 30 16:39:43 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4246020", acknowledgement = ack-nhfb, book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220", fjournal = "Electronics Letters", } @Article{Ayoub:1968:EKR, author = "F. Ayoub", title = "Encryption with keyed random permutations", journal = j-ELECT-LETTERS, volume = "17", number = "??", pages = "583--585", month = feb, year = "1968", CODEN = "ELLEAK", DOI = "https://doi.org/10.1049/el:19810411", ISSN = "0013-5194 (print), 1350-911X (electronic)", ISSN-L = "0013-5194", bibdate = "Fri Dec 30 16:39:40 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245887", acknowledgement = ack-nhfb, book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220", fjournal = "Electronics Letters", } @Article{Bell:1968:ANR, author = "James R. Bell", title = "{Algorithm 334}: {Normal} Random Deviates [{G5}]", journal = j-CACM, volume = "11", number = "7", pages = "498--498", month = jul, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:20 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See also \cite{Tracht:1982:RAN}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator); probability functions", } @Book{Berlekamp:1968:ACT, author = "Elwyn R. Berlekamp", title = "Algebraic coding theory", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xiv + 466", year = "1968", LCCN = "QA268 .B46", bibdate = "Sat Mar 10 10:01:51 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "McGraw-Hill series in systems science", acknowledgement = ack-nhfb, remark = "This book, and \cite{Massey:1969:SRS}, are the origin of the Berlekamp--Massey algorithm for recovering parameters from bit streams from linear feedback shift register (LSFR) generators.", subject = "Coding theory", } @Book{Bradley:1968:RTR, author = "J. V. Bradley", title = "Runs tests of randomness", publisher = pub-PH, address = pub-PH:adr, pages = "????", year = "1968", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Mon Jan 16 22:12:33 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, xxnote = "Check: is this a book, or a book chapter, or a conference paper??", } @Book{David:1968:NCM, editor = "F. N. (Florence Nightingale) David", title = "Normal centroids, medians and scores for ordinal data", volume = "29", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "201", year = "1968", LCCN = "QA47 .T7 no. 29", bibdate = "Mon Jun 27 13:35:14 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "Tracts for Computers", acknowledgement = ack-nhfb, editor-dates = "1909--1993", subject = "Mathematical statistics; Tables", } @Article{Dieter:1968:AME, author = "Ulrich Dieter", title = "{Autokorrelation multiplikativ erzeugter Pseudo-Zufallszahlen}. ({German}) [{Autocorrelation} generated multiplicative pseudo-random numbers]", journal = j-OPER-RES-VERFAHREN, volume = "6", number = "??", pages = "69--85", month = "????", year = "1968", CODEN = "ORVEAI", ISSN = "0078-5318", bibdate = "Fri Jan 6 10:19:53 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "{Operations Research-Verfahren}", language = "German", } @Article{Forsythe:1968:RNG, author = "A. B. Forsythe", title = "Random number generators", journal = j-COMPUT-AND-BIOMED-RES, volume = "1", number = "??", pages = "470--474", month = "????", year = "1968", CODEN = "CBMRB7", ISSN = "0010-4809 (print), 1090-2368 (electronic)", ISSN-L = "0010-4809", bibdate = "Mon Jan 16 22:13:27 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Computers and Biomedical Research", } @Article{Gardner:1968:MRS, author = "Martin Gardner", title = "On the meaning of randomness and some ways of achieving it", journal = j-SCI-AMER, volume = "??", number = "??", pages = "116--121", month = jul, year = "1968", CODEN = "SCAMAC", ISSN = "0036-8733 (print), 1946-7087 (electronic)", ISSN-L = "0036-8733", bibdate = "Mon Jan 16 22:15:01 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Scientific American", journal-URL = "http://www.nature.com/scientificamerican", } @Article{Good:1968:GST, author = "I. J. Good and T. N. Gover", title = "The generalized serial test and the binary expansion of $ \sqrt {2} $", journal = j-J-R-STAT-SOC-SER-A-GENERAL, volume = "131", number = "??", pages = "434--434", month = "????", year = "1968", CODEN = "JSSAEF", ISSN = "0035-9238", bibdate = "Sat Jan 07 11:23:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Good:1967:GST}.", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series A (General)", journal-URL = "http://www.jstor.org/journals/00359238.html", } @Article{Good:1968:RHP, author = "I. J. Good and R. F. Churchhouse", title = "The {Riemann} Hypothesis and Pseudorandom Features of the {M{\"o}bius} Sequence", journal = j-MATH-COMPUT, volume = "22", number = "104", pages = "857--861", month = oct, year = "1968", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", URL = "http://www.jstor.org/stable/pdfplus/2004584.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Book{Green:1968:TRP, author = "J. W. (John William) Green", title = "Tables of random permutations", publisher = "Department of National Development, Forestry and Timber Bureau", address = "Canberra, ACT, Australia", pages = "161", year = "1968", LCCN = "SD110 .A33 no. 44", bibdate = "Thu Mar 1 08:41:02 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Permutations; Tables", } @Article{Gregory:1968:GRP, author = "G. Gregory and K. Sharpe", title = "A Generalization of the Rejection Procedure for the Generation of Random Variables", journal = j-AUSTRALIAN-COMP-J, volume = "1", number = "3", pages = "169--172", year = "1968", CODEN = "ACMJB2", ISSN = "0004-8917", bibdate = "Fri Mar 09 17:54:03 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "It is shown how the simple rejection procedure may be generalized to cover the situation in which the range of the variable is infinite, subject to some mild restrictions. Methods for making the most efficient use of this generalized procedure are also discussed.", acknowledgement = ack-nhfb, fjournal = "Australian Computer Journal", } @Article{Kruskal:1968:NNC, author = "William Kruskal", title = "Note on a Note by {C. S. Pillai}", journal = j-AMER-STAT, volume = "22", number = "5", pages = "24--25", month = dec, year = "1968", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326357; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Pillai:1968:NEI}.", URL = "http://www.jstor.org/stable/2681837", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Lindholm:1968:APR, author = "J. H. Lindholm", title = "An Analysis of the Pseudo-Randomness Properties of Subsequences of Long $m$-Sequences", journal = j-IEEE-TRANS-INF-THEORY, volume = "IT-14", number = "4", pages = "569--576", year = "1968", CODEN = "IETTAW", DOI = "https://doi.org/10.1109/TIT.1968.1054188", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", bibdate = "Mon Feb 20 15:43:15 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Information Theory", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18", } @TechReport{Marsaglia:1968:OLRa, author = "George Marsaglia and T. A. Bray", title = "One-line random number generators and their use in combinations", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "12", month = mar, year = "1968", bibdate = "Wed Nov 12 07:42:28 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0667956", abstract = "This is a discussion of some one-line random number generators, requiring a single FORTRAN instruction, together with a description of some short FORTRAN programs which mix several such generators. Evidence suggesting that the simple congruential generators are unsatisfactory continues to grow; one of the most promising alternatives is to mix several simple generators. These composite generators do better in various tests for randomness than do the simple congruential generators used at many computer centers.", acknowledgement = ack-nhfb, } @Article{Marsaglia:1968:OLRb, author = "George Marsaglia and T. A. Bray", title = "One-line random number generators and their use in combinations", journal = j-CACM, volume = "11", number = "11", pages = "757--759", month = nov, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.15", MRnumber = "39\#5040", MRreviewer = "R. R. Coveyou", bibdate = "Fri Nov 25 18:20:22 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", ZMnumber = "0164.18802", abstract = "Some one-line random number generators, i.e. generators requiring a single FORTRAN instruction are discussed, and some short FORTRAN programs which mix several such generators are described. The aim is to provide methods for incorporating random number generators directly in FORTRAN programs, by means of a few in-line instructions. The advantages are speed (avoiding linkage to and from a subroutine), convenience, and versatility. Anyone wishing to experiment with generators, either using congruential generators by themselves or mixing several generators to provide a composite with potentially better statistical properties than the library generators currently available, may wish to consider some of the simple FORTRAN program discussed here.", acknowledgement = ack-nhfb, classcodes = "C6150E (General utility programs)", corpsource = "Boeing Scientific Research Lab., Seattle, WA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "FORTRAN; Monte Carlo; numerical analysis; PRNG (pseudo-random number generator); random number generation; simulation; utility programs", ZMreviewer = "R. R. Coveyou", } @Article{Marsaglia:1968:QPR, author = "George Marsaglia", title = "Query 27: Pseudo Random Normal Numbers", journal = j-TECHNOMETRICS, volume = "10", number = "2", pages = "401--402", month = may, year = "1968", CODEN = "TCMTA2", ISSN = "0040-1706 (print), 1537-2723 (electronic)", ISSN-L = "0040-1706", bibdate = "Tue Jun 21 19:29:12 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/1267057", acknowledgement = ack-nhfb, fjournal = "Technometrics", journal-URL = "http://www.jstor.org/journals/00401706.html; http://www.tandfonline.com/loi/utch20", } @Article{Marsaglia:1968:RNF, author = "George Marsaglia", title = "Random numbers fall mainly in the planes", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "61", number = "1", pages = "25--28", day = "15", month = sep, year = "1968", CODEN = "PNASA6", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "65.15", MRnumber = "38 #3998; 235695", bibdate = "Thu Nov 14 11:39:48 2002", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "A popularized account of this work appeared as ``Are random numbers really random?'' [Scientific Research (Philadelphia, PA), 3 (1968), 21--??]. This widely-cited paper describes the hyperplane problem that linear congruential generators suffer from, although careful choice of multipliers can minimize its importance: see \cite{Coveyou:1967:FAU,Dyadkin:1997:SBM,Dyadkin:1997:FEL,Dyadkin:2000:SBM}.", ZMnumber = "0172.21002", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/search", } @Article{Matthews:1968:GPN, author = "S. B. Matthews", title = "Generation of Pseudorandom Noise Having a {Gaussian} Spectral Density", journal = j-IEEE-TRANS-COMPUT, volume = "C-17", number = "4", pages = "382--385", month = apr, year = "1968", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/TC.1968.229387", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 17:40:48 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687351", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Meijer:1968:DASa, author = "H. G. Meijer", title = "The discrepancy of a {$G$}-adic sequence", journal = "Nederl. Akad. Wetensch, Proc. Ser. A", volume = "71", number = "??", pages = "54--66", month = "????", year = "1968", CODEN = "????", ISSN = "????", bibdate = "Thu Jan 19 07:11:08 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "Zbl 0155.37801", acknowledgement = ack-nhfb, fjournal = "Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae", } @Article{Meijer:1968:DASb, author = "H. G. Meijer", title = "The discrepancy of a $g$-adic sequence", journal = j-INDAG-MATH, volume = "30", number = "??", pages = "54--66", month = "????", year = "1968", CODEN = "IMTHBJ", ISSN = "0019-3577, 0023-3358", ISSN-L = "0019-3577", MRnumber = "MR 228450", bibdate = "Thu Jan 19 07:11:08 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Indagationes Mathematic{\ae}", } @Article{Millenson:1968:HRN, author = "J. R. Millenson and G. D. Sullivan", title = "A hardware random number generator for use with computer control of probabilistic contingencies", journal = j-BEHAV-RES-METH-INSTR, volume = "1", number = "5", pages = "194--196", month = jan, year = "1968", CODEN = "BRMIAC", DOI = "https://doi.org/10.3758/BF03207980", ISSN = "0005-7878", bibdate = "Fri Mar 09 07:35:51 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/content/l6q4517x00r56955/", acknowledgement = ack-nhfb, fjournal = "Behavior Research Methods and Instrumentation", keywords = "true random numbers from physical sources", } @Article{Miller:1968:ACP, author = "J. C. P. Miller and M. J. Prentice", title = "Additive congruential pseudo-random number generators", journal = j-COMP-J, volume = "11", number = "3", pages = "341--346", month = nov, year = "1968", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:51:30 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/compj1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/110341.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/tiff/341.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/tiff/342.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/tiff/343.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/tiff/344.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/tiff/345.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_11/Issue_03/tiff/346.tif", acknowledgement = ack-nhfb, classcodes = "C4190 (Other numerical methods)", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "numerical methods; random number generation", } @InCollection{Muller:1968:RN, author = "M. E. Muller", editor = "????", booktitle = "International Encyclopedia of Social Sciences", title = "Random Numbers", publisher = "????", address = "????", pages = "307--313", year = "1968", LCCN = "????", bibdate = "Sat Jan 07 11:58:15 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Pillai:1968:NEI, author = "C. S. Pillai", title = "A Note on the Expectation of an Irrational Function of a Random Variable", journal = j-AMER-STAT, volume = "22", number = "3", pages = "31--31", month = jun, year = "1968", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 09:31:38 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326355; https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See note \cite{Kruskal:1968:NNC}.", URL = "http://www.jstor.org/stable/2681808", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Polljak:1968:APN, author = "Ju. G. Polljak", title = "On the analysis of pseudorandom numbers", journal = "Avtomat. i Vy\v cisl. Tehn.", volume = "5", number = "??", pages = "31--35", month = "????", year = "1968", CODEN = "????", ISSN = "0132-4160", MRclass = "65.15", MRnumber = "MR 286248", bibdate = "Thu Jan 19 08:06:26 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Avt. i Vy{\v{c}}isl. Tehn.", fjournal = "Akademija Nauk Latvi\u\i sko\u\i\ SSR. Avtomatika i Vy\v cislitel\cprime naja Tehnika", language = "Russian", } @Article{Show:1968:AGR, author = "Richard H. Show", title = "{Algorithm 342}: {Generator} of random numbers satisfying the {Poisson} distribution", journal = j-CACM, volume = "11", number = "12", pages = "819--820", month = dec, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:23 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Sibuya:1968:GDE, author = "M. Sibuya", title = "Generating doubly exponential random numbers", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "5", number = "??", pages = "1--7", year = "1968", CODEN = "AISXAD", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", MRclass = "60.90", MRnumber = "MR0238412 (38 #6688)", MRreviewer = "M. Muller", bibdate = "Thu Mar 08 21:23:01 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Annals of the Institute of Statistical Mathematics, Supplement 5", fjournal = "Annals of the Institute of Statistical Mathematics (Tokyo)", journal-URL = "http://link.springer.com/journal/10463", } @Article{Snow:1968:AGR, author = "R. H. Snow", title = "{Algorithm 342}: {Generator} of Random Numbers Satisfying the {Poisson} Distribution [{G5}]", journal = j-CACM, volume = "11", number = "12", pages = "819--820", month = dec, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Mar 24 21:38:51 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "ITT Research Inst., Chicago, IL, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "complete computer programs; Monte Carlo methods; number generation; PRNG (pseudo-random number generator); random; subroutines", } @Article{Whittlesey:1968:CCB, author = "John R. B. Whittlesey", title = "A comparison of the correlational behavior of random number generators for the {IBM 360}", journal = j-CACM, volume = "11", number = "9", pages = "641--644", month = sep, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.15", MRnumber = "MR 255011 (40\#8218)", bibdate = "Fri Nov 25 18:20:21 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See implementation \cite{Fellen:1969:LEI}.", abstract = "Hutchinson states that the ``new'' (prime modulo) multiplicative congruential pseudorandom generator, attributed to D. H. Lehmer, has passed the usual statistical tests for random number generators. It is here empirically shown that generators of this type can produce sequences whose autocorrelation functions up to lag 50 exhibit evidence of nonrandomness for many multiplicative constants. An alternative generator proposed by Tausworthe, which uses irreducible polynomials over the field of characteristic two, is shown to be free from this defect. The applicability of these two generators to the IBM 360 is then discussed. Since computer word size can affect a generator's statistical behavior the older mixed and simple congruential generators, although extensively tested on computers having 36 or more bits per word, may not be optimum generators for the IBM 360.", acknowledgement = ack-nhfb, country = "USA", descriptors = "Tausworthe generator; RNG; test; comparison; runtime/storage efficiency; linear congruential generator; shift register sequences", enum = "3287", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "32-bit versus 36-bit word size; autocorrelation function; congruential generators; digital shift-register generators; IBM 360; IBM S/360; irreducible polynomials; linear recurrence modulo two; prime numbers; primitive trinomials modulo two; PRNG (pseudo-random number generator); pseudorandom number generators; random numbers; serial correlation; statistical tests for randomness", references = "21", remark = "Hutchinson states that the ``new'' (prime modulo) multiplicative congruential pseudorandom generator, attributed to D. H. Lehmer, has passed the usual statistical tests for random number generators. It is here empirically shown that generators of this type can produce sequences whose autocorrelation functions up to lag 50 exhibit evidence of non-randomness for many multiplicative constants. an alternative generator proposed by Tausworthe, which us\ldots{}", ZMreviewer = "R. R. Coveyou", } @Article{Zaremba:1968:GLP, author = "S. C. Zaremba", title = "Good lattice points in the sense of {Hlawka} and {Monte Carlo} integration", journal = j-MONAT-MATH, volume = "72", number = "3", pages = "264--269", month = jun, year = "1968", CODEN = "MNMTA2", DOI = "https://doi.org/10.1007/BF01362552", ISSN = "0026-9255 (print), 1436-5081 (electronic)", ISSN-L = "0026-9255", MRclass = "65.15", MRnumber = "0228155 (37 \#3739)", MRreviewer = "J. Spanier", bibdate = "Thu Jan 19 08:34:10 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/content/j48m46451580607q/", acknowledgement = ack-nhfb, fjournal = "Monatshefte f{\"u}r Mathematik", journal-URL = "http://link.springer.com/journal/605", } @Article{Zaremba:1968:MBM, author = "S. K. Zaremba", title = "The Mathematical Basis of {Monte Carlo} and Quasi-{Monte Carlo} Methods", journal = j-SIAM-REVIEW, volume = "10", number = "3", pages = "303--314", month = jul, year = "1968", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1010056", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRnumber = "233489", bibdate = "Thu Mar 27 09:05:58 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/10/3; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://www.jstor.org/stable/2027655", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "July 1968", } @Article{Beasley:1969:DTS, author = "J. D. Beasley and K. Wilson", title = "Design and testing of the {System 4} random number generator", journal = j-COMP-J, volume = "12", number = "4", pages = "368--372", month = nov, year = "1969", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:51:40 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/compj1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/120368.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/368.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/369.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/370.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/371.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/372.tif", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "random number generation", } @Article{Bell:1969:DFT, author = "C. B. Bell and J. F. Donoghue", title = "Distribution-free tests of randomness", journal = j-SANKHYA-A, volume = "31", number = "??", pages = "157--176", month = "????", year = "1969", CODEN = "SANABS", ISSN = "0036-4452", bibdate = "Mon Jan 16 22:07:31 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series A. Methods and Techniques", } @Article{Chaitin:1969:LPC, author = "Gregory J. Chaitin", title = "On the Length of Programs for Computing Finite Binary Sequences: {Statistical} Considerations", journal = j-J-ACM, volume = "16", number = "1", pages = "145--159", month = jan, year = "1969", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321495.321506", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Sat Oct 22 22:05:56 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "An attempt is made to carry out a program (outlined in a previous paper) for defining the concept of a random or patternless, finite binary sequence, and for subsequently defining a random or patternless, infinite binary sequence to be a sequence whose initial segments are all random or patternless finite binary sequences. A definition based on the bounded-transfer Turing machine is given detailed study, but insufficient understanding of this computing machine precludes a complete treatment. A computing machine is introduced which avoids these difficulties.", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @InProceedings{Coveyou:1969:RNG, author = "R. R. Coveyou", title = "Random number generation is too important to be left to chance", crossref = "Anonymous:1969:CPP", pages = "70--111", year = "1969", LCCN = "QA1 S565 v. 3", bibdate = "Thu Jan 12 17:50:36 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, remark = "The clever title of this paper is widely cited on the Internet, but the contents are heavily mathematical. On page 108, section 12, the author remarks ``There is at present no RNG known to be superior to an SLCRNG [simple linear congruential random number generator] with a carefully chosen multiplier $ \lambda $. The choice of addend $ \mu $ is not of great importance.'' The reference is to a generator of the form $ x_{n + 1} = (\lambda x_x + \mu) \bmod P $, and page 93 gives conditions on the parameters $ \lambda $ and $ \mu $ for reaching maximal period $P$. However, since this paper was written, many much better generators have been found. In the same section, Coveyou says ``reports of {\em good\/} performance of RNG, not supported by theory, must be deemed irrelevant.'' Pages 108--110 contain critical comments on entry \cite{Zaremba:1969:MBM}.", } @Article{Cunsolo:1969:CNP, author = "D. Cunsolo", title = "Costruzione di numeri pseudorandom con periodo superiore alla base $m$. ({Italian}) [Generation of pseudorandom numbers with period greater than the base $m$ ]", journal = j-CALCOLO, volume = "6", number = "1", pages = "69--85", month = mar, year = "1969", CODEN = "CALOBK", DOI = "https://doi.org/10.1007/BF02576125", ISSN = "0008-0624 (print), 1126-5434 (electronic)", ISSN-L = "0008-0624", bibdate = "Mon Jan 16 22:08:25 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/content/60u464k30851uj27/", acknowledgement = ack-nhfb, fjournal = "Calcolo: a quarterly on numerical analysis and theory of computation", journal-URL = "http://link.springer.com/journal/10092", language = "Italian", remark = "From the English abstract: ``In the present study a modified method (of the linear congruential generator, $ x_{n + 1} = (a x_n + b) \bmod m $ ) is proposed in order to increase this period up to values of $ M \approx m^2 $. The modified method consists in a systematic variation of the parameter $b$, with a period conveniently different from $m$''.", } @TechReport{Deo:1969:APN, author = "N. Deo and D. Rubin", title = "An additive pseudorandom number generator with semi-infinite sequence length", type = "Report", institution = "NASA", address = "????", pages = "4", year = "1969", bibdate = "Thu Jan 19 17:27:40 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Document ID 19700050209.", acknowledgement = ack-nhfb, remark = "U. of Hawaii, Hawaii International Conference on System Sciences, 2nd, U. of Hawaii; 2nd; Jan. 22--24, 1969; Honolulu, HI", } @Article{Dieter:1969:AME, author = "Ulrich Dieter", title = "{Autokcorrelation multiplikativ erzeugter Pseudo-Zufallszahlen}. ({German}) [{Autocorrelation} in multiplicatively-generated pseudorandom numbers]", journal = j-OPER-RES-VERFAHREN, volume = "6", number = "??", pages = "69--85", month = "????", year = "1969", CODEN = "ORVEAI", ISSN = "0078-5318", bibdate = "Mon Jan 16 22:09:26 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "{Operations Research-Verfahren}", language = "German", } @Article{Donnelly:1969:STU, author = "T. Donnelly", title = "Some techniques for using pseudorandom numbers in computer simulation", journal = j-CACM, volume = "12", number = "7", pages = "392--394", month = jul, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:27 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C1220 (Simulation, modelling and identification); C4190 (Other numerical methods)", corpsource = "Univ. North Carolina, Chapel Hill, NC, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "numerical methods; PRNG (pseudo-random number generator); simulation", } @Article{Downham:1969:RT, author = "D. Y. Downham", title = "The runs up and down test", journal = j-COMP-J, volume = "12", number = "4", pages = "373--376", month = nov, year = "1969", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:51:40 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/compj1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/120373.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/373.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/374.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/375.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/376.tif", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "random number generation", } @Article{Fellen:1969:LEI, author = "Bryna M. Fellen", title = "Letter to the {Editor}: an implementation of the {Tausworthe} generator", journal = j-CACM, volume = "12", number = "7", pages = "413--413", month = jul, year = "1969", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/363156.363194", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:27 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Whittlesey:1968:CCB}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Good:1969:HRR, author = "I. J. Good", title = "How random are random numbers?", journal = j-AMER-STAT, volume = "23", number = "4", pages = "42--45", month = oct, year = "1969", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Thu Jan 05 17:41:34 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2681742", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", remark = "The prolific author I. J. Good (his `shorter publications list' available on the Web lists 2378 of his publications) reports in \cite[page 43, column 2]{Good:1969:HRR} ``This method [the multiplicative congruential generator] was proposed by the writer in a classified paper in 1948 and [independently] by Lehmer \cite{Lehmer:1951:MML} [the proceedings of a September 1949 conference].'' See also the remark from this paper in entry \cite{Good:1950:PWE}.", } @Article{Grosenbaugh:1969:MFR, author = "L. R. Grosenbaugh", title = "More on {Fortran} random number generators", journal = j-CACM, volume = "12", number = "11", pages = "639--639", month = nov, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:28 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", } @Article{Gubenko:1969:FPR, author = "V. S. Gubenko and N. E. Kirillov and K. A. Me{\v{s}}kovski{\u\i} and A. I. {\v{C}}erkunov", title = "Formation of pseudo-random uniformly distributed numbers from noise-like signals", journal = "Izv. Akad. Nauk SSSR Tehn. Kibernet.", volume = "1", number = "??", pages = "57--63", month = "????", year = "1969", CODEN = "????", ISSN = "????", bibdate = "Thu Jan 19 06:54:38 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Hemmerle:1969:GPN, author = "W. J. Hemmerle", title = "Generating pseudorandom numbers on a two's complement machine such as the {IBM 360}", journal = j-CACM, volume = "12", number = "7", pages = "382--383", month = jul, year = "1969", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/363156.363166", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:27 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "The familiar multiplicative congruential generator is examined in the context of the type of two's complement arithmetic used in the IBM 360 series. Different sequences of residues are considered and relationships established among them. It is shown that a sequence of positive and negative residues may be produced more simply and economically than with the conventional approach and yet have twice the period of the latter without loss of desirable statistical properties. Another easily generated sequence involving absolute values is also shown to have twice the period but with the less attractive statistical properties. The statistical properties of these sequences are given and related to previously established criteria.", acknowledgement = ack-nhfb, classcodes = "C5230 (Digital arithmetic methods); C7890 (Other special applications of computing)", corpsource = "Univ. Rhode Island, Kingston, RI, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "digital arithmetic; IBM S/360; PRNG (pseudo-random number generator); random number generation", } @Article{Knop:1969:RAG, author = "R. Knop", title = "Remark on {Algorithm 334} [{G5}]: {Normal} random deviates", journal = j-CACM, volume = "12", number = "5", pages = "281--281", month = may, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:26 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, country = "USA", descriptors = "RVG", enum = "7513", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", references = "0", } @Article{Kruskal:1969:EPR, author = "J. B. Kruskal", title = "Extremely Portable Random Number Generator", journal = j-CACM, volume = "12", number = "2", pages = "93--94", month = feb, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:24 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "Extremely portable subroutines are sometimes needed for which moderate quality and efficiency suffice. Typically, this occurs for library functions (like random number generation and in core sorting) which are not entirely universal or are not used in a standardized way. The literature on random number generators does not seem to contain an algorithm that meets requirements of this sort. An extremely portable 8-line FORTRAN program is provided which based on an important paper by Coveyou and MacPherson (1967).Using their methods, Fourier analysis is applied to the probability function for the consecutive n-tuples provided by our generator (with $n$ less than or equal to 4). While the small modulus which must be used to maintain portability prevents the quality of the generator from being high, the generator compares well with the bounds established in the above mentioned paper.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Bell Telephone Lab. Inc., Murray Hill, NJ, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "linear sequential generators; PRNG (pseudo-random number generator); pseudo random numbers; random generators; random number analysis; random number generation; random number generators; random number program; random numbers; subroutines", } @Article{Lee:1969:ECF, author = "W. C. Y. Lee", title = "An extended correlation function of two random variables applied to mobile radio transmission", journal = j-BELL-SYST-TECH-J, volume = "48", number = "10", pages = "3423--3440", month = dec, year = "1969", CODEN = "BSTJAN", ISSN = "0005-8580", MRclass = "94.10", MRnumber = "0261999 (41 \#6609)", MRreviewer = "P. M. Lee", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4810.html; http://www.alcatel-lucent.com/bstj/vol48-1969/bstj-vol48-issue10.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See erratum \cite{Anonymous:1970:EWC}.", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-10-3423.pdf; http://www.alcatel-lucent.com/bstj/vol48-1969/articles/bstj48-10-3423.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Lehmer:1969:BRR, author = "D. H. Lehmer", title = "Book Review: {{\booktitle{Random number generators}} by Birger Jansson}", journal = j-QUART-APPL-MATH, volume = "27", number = "3", pages = "421--421", year = "1969", CODEN = "QAMAAY", DOI = "https://doi.org/10.2307/43636000", ISSN = "0033-569X (print), 1552-4485 (electronic)", ISSN-L = "0033-569X", bibdate = "Mon Jan 31 10:50:30 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/43636000", acknowledgement = ack-nhfb, fjournal = "Quarterly of Applied Mathematics", journal-URL = "http://dl.acm.org/citation.cfm?id=J641; http://www.ams.org/journals/qam", reviewed-author = "Birger Jansson", } @Article{Lewis:1969:PNG, author = "P. A. W. Lewis and A. S. Goodman and J. M. Miller", title = "A pseudorandom number generator for the {SYSTEM\slash 360}", journal = j-IBM-SYS-J, volume = "8", number = "2", pages = "136--146", year = "1969", CODEN = "IBMSA7", ISSN = "0018-8670", bibdate = "Tue Mar 19 17:38:46 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "IBM Systems Journal", } @TechReport{Marsaglia:1969:OSA, author = "George Marsaglia", title = "One-Sided Approximations by Linear Combinations of Functions", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "18", month = sep, year = "1969", bibdate = "Wed Nov 12 07:42:28 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0695796", abstract = "The paper discusses how to approximate a function $ g(x) $ from one side by a linear combination of functions $ f_1 (x), \ldots {}, f_n(x) $ so as to minimize the area between the two. It discusses the problem as one of finding the point where a moving hyperplane last touches a convex set and an approximate procedure based on linear programming methods. It gives details of an algorithm for solving the problem, examples, and applications to Monte Carlo Theory --- generating random variables in a computer.", acknowledgement = ack-nhfb, } @TechReport{Marsaglia:1969:RCR, author = "George Marsaglia", title = "Regularities in congruential random number generators", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "8", month = may, year = "1969", bibdate = "Wed Nov 12 07:42:28 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0689295", abstract = "The paper suggests that points in $n$-space produced by congruential random number generators are too regular for general Monte Carlo use. Regularity was established previously for multiplicative congruential generators by showing that all the points fall in sets of relatively few parallel hyperplanes. The existence of many containing sets of parallel hyperplanes was easily established, but proof that the number of hyperplanes was small required a result of Minkowski from the geometry of numbers --- a symmetric, convex set of volume 2 to the nth power must contain at least two points with integral coordinates. The present paper takes a different approach to establishing the course lattice structure of congruential generators. It gives a simple, self-contained proof that points in $n$-space produced by the general congruential generator $ r_(i + 1)$ is identically equal to $ a(r_i) + b \bmod m$ must fall on a lattice with unit-cell volume at least $m$ to the power $ (n - 1)$. There is no restriction on $a$ or $b$; this means that all congruential random number generators must be considered unsatisfactory in terms of lattices containing the points they produce, for a good generator of random integers should have an $n$-lattice with unit-cell volume 1.", acknowledgement = ack-nhfb, } @Article{Martin-Lof:1969:AR, author = "P. Martin-L{\"o}f", title = "Algorithms and randomness", journal = j-REV-INST-INT-STATIST, volume = "37", number = "??", pages = "265--272", month = "????", year = "1969", CODEN = "????", ISSN = "0373-1138", bibdate = "Mon Jan 16 22:10:43 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Revue de l'Institut international de statistique = Review of the International Statistical Institute", } @Article{Massey:1969:SRS, author = "J. L. Massey", title = "Shift-Register Synthesis and {BCH} Decoding", journal = j-IEEE-TRANS-INF-THEORY, volume = "IT-15", number = "1", pages = "122--127", month = jan, year = "1969", CODEN = "IETTAW", DOI = "https://doi.org/10.1109/TIT.1969.1054260", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", bibdate = "Mon Jun 27 21:47:51 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Information Theory", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18", remark = "This paper, and \cite{Berlekamp:1968:ACT}, are the origin of the Berlekamp--Massey algorithm for recovering parameters from bit streams from linear feedback shift register (LSFR) generators.", } @Article{Meyer:1969:MGR, author = "D. L. Meyer", title = "Methods of generating random normal numbers", journal = j-EDU-PSYCH-MEASUREMENT, volume = "29", number = "1", pages = "193--198", month = "????", year = "1969", CODEN = "EPMEAJ", ISSN = "0013-1644 (print), 1552-3888 (electronic)", ISSN-L = "0013-1644", bibdate = "Thu Mar 08 21:21:54 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Educational and Psychological Measurement", } @Article{Naylor:1969:BSG, author = "T. H. Naylor", title = "Bibliography 19: Simulation and gaming", journal = j-COMP-REV, volume = "10", number = "??", pages = "61--69", month = "????", year = "1969", CODEN = "CPGRA6", ISSN = "0010-4884, 0149-1202", ISSN-L = "0010-4884", bibdate = "Thu Jan 19 07:22:16 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Computing Reviews", } @Article{Passaquindici:1969:MMC, author = "Maria Passaquindici", title = "{I} metodi di {Monte Carlo} e la generazione dei numeri casuali. ({Italian}) [{Monte Carlo} methods and the generation of random numbers]", journal = j-METRON, volume = "27", number = "3--4", pages = "88--112, i--viii. (2 foldouts)", month = "????", year = "1969", CODEN = "MRONAM", ISSN = "0026-1424 (print), 2281-695X (electronic)", ISSN-L = "0026-1424", MRclass = "65C10", MRnumber = "324869", MRreviewer = "E. Bareiss", bibdate = "Sun Jul 5 08:55:46 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/metron1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0204.51501", acknowledgement = ack-nhfb, fjournal = "Metron", journal-URL = "https://www.springer.com/journal/40300", language = "Italian", ZMnumber = "03325334", } @Article{Payne:1969:CLP, author = "W. H. Payne and J. R. Rabung and T. P. Bogyo", title = "Coding the {Lehmer} pseudo-random number generator", journal = j-CACM, volume = "12", number = "2", pages = "85--86", month = feb, year = "1969", CODEN = "CACMA2", DOI = "https://doi.org/10.1145/362848.362860", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:24 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "An algorithm and coding technique is presented for quick evaluation of the Lehmer pseudo-random number generator modulo $ 2^{31} - 1 $, a prime Mersenne number which produces $ 2^{31} - 2 $ numbers, on a $p$-bit (greater than $ 31 $ ) computer. The computation method is extendible to limited problems in modular arithmetic. Prime factorization for $ 2^{61} - 2 $ and a primitive root for $ 2^{61} - 1 $, the next largest prime Mersenne number, are given for possible construction of a pseudo-random number generator of increased cycle length.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Washington State Univ., Pullman, WA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "modular arithmetic; prime factorization; primitive roots; PRNG (pseudo-random number generator); programming; pseudo-random number; random number; random number generation; simulation; uniform frequency function; uniform probability density", } @Article{Seraphin:1969:NAF, author = "Dominic S. Seraphin", title = "Numerical Analysis: a fast random number generator for {IBM 360}", journal = j-CACM, volume = "12", number = "12", pages = "695--695", month = dec, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:29 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "State Univ. New York, Stony Brook, NY, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "IBM S/360; PRNG (pseudo-random number generator); random number generation; subroutines", } @Article{Verdier:1969:RWS, author = "P. H. Verdier", title = "Relations within sequences of congruential pseudorandom numbers", journal = j-J-RES-NATL-BUR-STAND-B, volume = "73", number = "??", pages = "41--44", month = "????", year = "1969", CODEN = "JNBBAU", ISSN = "0022-4340", bibdate = "Mon Jan 16 22:11:30 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Research of the National Bureau of Standards. Section B, Mathematics and Mathematical Physics", journal-URL = "http://www.nist.gov/nvl/jrespastpapers.cfm", } @Article{Whittlesey:1969:LEM, author = "John R. B. Whittlesey", title = "Letter to the {Editor}: {On} the Multidimensional Uniformity of Pseudorandom Generators", journal = j-CACM, volume = "12", number = "5", pages = "247--247", month = may, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:26 MST 2005", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Marsaglia:1968:RNF}.", acknowledgement = ack-nhfb, annote = "It would appear that George Marsaglia's recent article proving that all the pseudorandom points generated in the unit n-cube ``will be found to lie in a relatively small number of parallel hyperplanes'' has given the coup de grace, to the use of multiplicative congruential generators in all Monte Carlo applications, except those having the most non-stringent requirements for multidimensional uniformity.", country = "USA", descriptors = "Comparison; shift register sequences; Tausworthe generator; RNG; test; multidimensional uniformity; grid structure; linear congruential generator", enum = "3286", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", references = "7", remark = "It would appear that George Marsaglia's recent article proving that all the pseudorandom points generated in the unit n-cube ``will be found to lie in a relatively small number of parallel hyperplanes'' has given the coup de grace, to the use of multiplicative congruential generators in all Monte Carlo applications, except those having the most non-stringent requirements for multidimensional uniformity.", } @InProceedings{Zaremba:1969:MBM, author = "S. K. Zaremba", title = "The Mathematical Basis of {Monte Carlo} and quasi-{Monte Carlo} Methods", crossref = "Anonymous:1969:CPP", pages = "1--12", year = "1969", LCCN = "QA1 S565 v. 3", bibdate = "Thu Jan 12 17:50:36 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See critical comments in \cite[pages 108--110]{Coveyou:1969:RNG}.", acknowledgement = ack-nhfb, } @Article{Ahrens:1970:PRN, author = "J. H. Ahrens and Ulrich Dieter and A. Grube", title = "Pseudo-Random Numbers. {A} New Proposal for the Choice of Multiplicators", journal = j-COMPUTING, volume = "6", number = "1--2", pages = "121--138", month = mar, year = "1970", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", bibdate = "Tue Jan 2 17:40:51 MST 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; INSPEC Axiom database (1968--date)", acknowledgement = ack-ec # " and " # ack-nhfb, affiliation = "Nova Scotia Tech. Coll., Halifax, NS, Canada", classification = "C7890", description = "random number generation; subroutines", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", keywords = "ALGOL subroutines; autocorrelation of sequence; choice of multiplicators; FORTRAN subroutines; pseudo-random numbers", } @Article{Anonymous:1970:EWC, author = "Anonymous", title = "Erratum: {W. C. Y. Lee, {\em An extended correlation function of two random variables applied to mobile radio transmission}, BSTJ {\bf 48}(10) 3423--3440 (1969)}", journal = j-BELL-SYST-TECH-J, volume = "49", number = "2", pages = "320--320", month = feb, year = "1970", CODEN = "BSTJAN", ISSN = "0005-8580", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4902.html; http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue02.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Lee:1969:ECF}.", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-2-320.pdf; http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-2-320.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @TechReport{Anonymous:1970:FVP, author = "Anonymous", title = "A {Fortran V} package for testing and anaylsis of pseudorandom number generators", type = "Technical report", number = "CP-700011", institution = "Computer Science/Operations Research Center, Institute of Technology, Southern Methodist University", address = "Dallas, TX, USA", pages = "32", year = "1970", bibdate = "Fri Feb 09 17:44:49 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Behboodian:1970:ERV, author = "Javad Behboodian", title = "On the Expectation of the Random Variable {$ (X^2 - Y^2)^{1 / 2} $}", journal = j-AMER-STAT, volume = "24", number = "4", pages = "28--29", month = oct, year = "1970", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 10:52:19 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326366; https://www.math.utah.edu/pub/tex/bib/amstat1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2681312", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Blaisdell:1970:RSP, author = "B. E. Blaisdell and H. Solomon", title = "On random sequential packing in the plane and a conjecture of {Pal{\'a}sti}", journal = j-J-APPL-PROBAB, volume = "7", number = "3", pages = "667--689", month = dec, year = "1970", CODEN = "JPRBAM", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", bibdate = "Wed Feb 29 21:17:55 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/kepler.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/3211946", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", journal-URL = "http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/", keywords = "parking-lot test; sphere packing", } @Article{Butler:1970:AAG, author = "E. L. Butler", title = "{ACM Algorithm 370}: General Random Number Generator", journal = j-CACM, volume = "13", number = "1", pages = "49--52", month = jan, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See remark \cite{Proll:1972:RAA}.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Texas A and M Univ., College Station, TX, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "random number generation; subroutines", } @Article{Cenacchi:1970:PRN, author = "G. Cenacchi and A. {De Matteis}", title = "Pseudo-random numbers for comparative {Monte Carlo} calculations", journal = j-NUM-MATH, volume = "16", number = "1", pages = "11--15", month = feb, year = "1970", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF02162402", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/nummath.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "To compare the results of two slightly different situations in a given problem solved by the Monte Carlo method it is convenient to use the same random numbers in both cases. To facilitate the reproducibility of the random numbers used a method based on two pseudo-random number generators may be adopted. In this paper the method is discussed with reference to multiplicative congruential generators, the influence of the initial value on a random sequence obtained by a given multiplier being examined first.", acknowledgement = ack-nhfb, classification = "C1140G (Monte Carlo methods); C7890 (Other special applications of computing)", corpsource = "CNEN, Bologna, Italy", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "Monte Carlo methods; random number generation", } @Article{Dixon:1970:NSE, author = "J. Dixon", title = "The number of steps in the {Euclidean} algorithm", journal = j-J-NUMBER-THEORY, volume = "2", number = "??", pages = "414--422", month = "????", year = "1970", CODEN = "JNUTA9", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Thu Dec 29 07:11:27 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Number Theory", } @Article{Downham:1970:SAA, author = "D. Y. Downham", title = "Statistical Algorithms: {Algorithm AS 29}: The Runs Up and Down Test", journal = j-APPL-STAT, volume = "19", number = "2", pages = "190--192", month = jun, year = "1970", CODEN = "APSTAG", ISSN = "0035-9254 (print), 1467-9876 (electronic)", ISSN-L = "0035-9254", bibdate = "Sat Apr 21 10:19:52 MDT 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", note = "See \cite{Wedderburn:1976:SAR}.", URL = "http://lib.stat.cmu.edu/apstat/29", acknowledgement = ack-nhfb, fjournal = "Applied Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues", } @Article{Fuchs:1970:EDR, author = "E. A. Fuchs and P. E. Jackson", title = "Estimates of Distributions of Random Variables for Certain Computer Communications Traffic Models", journal = j-CACM, volume = "13", number = "12", pages = "752--757", month = dec, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/network.bib; ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "Reproduced in Advances in Computer Commun., Chu, W. W., (Ed (1974), 2-7; in Computer Commun., Green, P. E., and Lucky, R. W. (Eds.), (1975), 577-582).", abstract = "A study of multiaccess computer communications has characterized the distributions underlying an elementary model of the user-computer interactive process. The model used is elementary in the sense that many of the random variables that generally are of interest in computer communications studies can be decomposed into the elements of this model. Data were examined from four operational multiaccess systems, and the model is shown to be robust; that is each of the variables of the model has the same distribution independent of which of the four systems is being examined. It is shown that the gamma distribution can be used to describe the discrete variables. Approximations to the gamma distribution by the exponential distribution are discussed for the systems studied.", acknowledgement = ack-nhfb, classcodes = "C4290 (Other computer theory)", corpsource = "Bell Telephone Labs. Inc., Holmdel, NJ, USA", descriptors = "Random Process; Computer Communication; Traffic Model; Distribution; Estimation", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "computation theory; computer communications; distribution of random variables; modelling; multi-access systems; multiaccess systems; operating systems; operating systems (computers); optimisation models; optimization models; time-sharing; time-sharing systems; user computer interactive processes", treatment = "T Theoretical or Mathematical", } @Article{Good:1970:RPM, author = "Irving John Good", title = "Review of {Philip McShane, \booktitle{Randomness, Statistics, and Emergence}, Gill and MacMillan, 1970}", journal = "Times Literary Supplement", volume = "??", number = "??", pages = "1043", day = "18", month = sep, year = "1970", bibdate = "Mon Nov 12 08:43:06 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See book \cite{McShane:1970:RSE}.", acknowledgement = ack-nhfb, } @Article{Gustavson:1970:FRN, author = "F. G. Gustavson and W. Liniger", title = "A Fast Random Number Generator with Good Statistical Properties", journal = j-COMPUTING, volume = "6", number = "3--4", pages = "221--226", year = "1970", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", bibdate = "Tue Jan 2 17:40:51 MST 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; INSPEC Axiom database (1968--date)", acknowledgement = ack-ec # " and " # ack-nhfb, affiliation = "IBM, Yorktown Heights, NY, USA", classification = "C7890", description = "random number generation", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", keywords = "calculation time reduction; division operation; IBM/360; overflow tests removal; random number generator; shift instructions; speed increasing; statistical properties", } @Article{Haber:1970:NEM, author = "Seymour Haber", title = "Numerical Evaluation of Multiple Integrals", journal = j-SIAM-REVIEW, volume = "12", number = "4", pages = "481--526", month = oct, year = "1970", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1012102", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:22 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/12/4; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://www.jstor.org/stable/2028488", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "October 1970", remark = "Tutorial on multidimensional Monte Carlo integration.", } @Article{Haber:1970:SNA, author = "Seymour Haber", title = "Sequences of Numbers That Are Approximately Completely Equidistributed", journal = j-J-ACM, volume = "17", number = "2", pages = "269--272", month = apr, year = "1970", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321574.321580", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Sun Nov 6 11:54:52 1994", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Halton:1970:RPS, author = "John H. Halton", title = "A Retrospective and Prospective Survey of the {Monte Carlo} Method", journal = j-SIAM-REVIEW, volume = "12", number = "1", pages = "1--63", month = "????", year = "1970", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1012001", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:14 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/12/1; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1970", } @Article{Harris:1970:AFG, author = "V. C. Harris", title = "An Algorithm for Finding the Greatest Common Divisor", journal = j-FIB-QUART, volume = "8", number = "1", pages = "102--103", month = feb, year = "1970", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:23 MDT 2011", bibsource = "http://www.fq.math.ca/8-1.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.fq.math.ca/Scanned/8-1/harris1.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Hastings:1970:MCS, author = "W. K. Hastings", title = "{Monte Carlo} Sampling Methods Using {Markov} Chains and Their Applications", journal = j-BIOMETRIKA, volume = "57", number = "1", pages = "97--109", month = apr, year = "1970", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2334940", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 14:33:36 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315464; https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib; https://www.math.utah.edu/pub/tex/bib/biometrika1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "This paper introduces what is now known as the Metropolis--Hastings algorithm, a generalization of the work in \cite{Metropolis:1953:ESC}. See \cite[page 255]{Hitchcock:2003:HMH}.", URL = "http://www.jstor.org/stable/2334940; http://www.probability.ca/hastings/", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://www.jstor.org/journals/00063444.html", keywords = "Metropolis--Hastings algorithm", } @Book{Johnson:1970:CUD, author = "Norman Lloyd Johnson and Samuel Kotz", title = "Continuous univariate distributions", publisher = "Hougton Mifflin", address = "New York, NY, USA", pages = "xiv + 300 (vol. 1), xiii + 306 (vol. 2)", year = "1970", LCCN = "QA273.6 .J6", MRclass = "62Exx, 62-02, 62E10, 62E15", bibdate = "Thu Mar 1 09:37:58 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "Distributions in statistics", ZMnumber = "Zbl 0213.21101", acknowledgement = ack-nhfb, subject = "distribution (probability theory)", } @Article{Juncosa:1970:BRBb, author = "Mario Juncosa", title = "Book Review: {{\booktitle{Random Number Generators}} (Birger Jansson)}", journal = j-SIAM-REVIEW, volume = "12", number = "2", publisher = "SIAM", pages = "310--311", month = "????", year = "1970", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1012068", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:17 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/12/2; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "http://link.aip.org/link/?SIR/12/310/1", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "April 1970", } @Article{Kale:1970:CNN, author = "B. K. Kale", title = "Classroom Notes: Normality of Linear Combinations of Non-Normal Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "77", number = "9", pages = "992--995", month = nov, year = "1970", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:07 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Knop:1970:AAR, author = "R. E. Knop", title = "{ACM Algorithm 381}: Random Vectors Uniform In Solid Angle", journal = j-CACM, volume = "13", number = "5", pages = "326--326", month = may, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See remark \cite{Schrack:1972:RAR}.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Rutgers Univ., New Brunswick, NJ, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "random number generation; subroutines", } @Article{Lempel:1970:HBG, author = "A. Lempel", title = "On a Homomorphism of the {de Bruijn} Graph and its Applications to the Design of Feedback Shift Registers", journal = j-IEEE-TRANS-COMPUT, volume = "C-19", number = "12", pages = "1204--1209", month = dec, year = "1970", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1970.222859", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 08:01:38 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671452", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @InCollection{Linder:1970:TTR, author = "Arthur Linder", title = "Testing a table of random numbers", crossref = "Bose:1970:EPS", pages = "469--478", year = "1970", bibdate = "Mon Jan 16 22:00:01 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "Zbl 0228.62003", acknowledgement = ack-nhfb, } @Article{Maritsas:1970:CSV, author = "D. G. Maritsas and M. G. Hartley", title = "A Case Study of a Versatile Generator of Repeatable Non-{Poisson} Sequences of Pseudorandom Pulses", journal = j-IEEE-TRANS-COMPUT, volume = "C-19", number = "10", pages = "924--938", month = oct, year = "1970", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1970.222800", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 08:01:37 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671393", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Maritsas:1970:DCG, author = "D. G. Maritsas and M. G. Hartley", title = "Design Criteria for a Generator of Repeatable Non-{Poisson} Sequences of Pseudorandom Pulses", journal = j-IEEE-TRANS-COMPUT, volume = "C-19", number = "9", pages = "812--817", month = sep, year = "1970", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1970.223045", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 08:01:36 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671638", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Marsaglia:1970:RCR, author = "George Marsaglia", title = "Regularities in congruential random number generators", journal = j-NUM-MATH, volume = "16", number = "1", pages = "8--10", month = feb, year = "1970", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.15", MRnumber = "42 \#8651; 273775", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", ZMnumber = "0212.18204", acknowledgement = ack-nhfb, classification = "C7890 (Other special applications of computing)", corpsource = "Boeing Sci. Res. Labs., Seattle, WA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "random number generation", xxyear = "1970/1971", ZMclass = "65C10 Random number generation", } @TechReport{Marsaglia:1970:RVI, author = "George Marsaglia", title = "Random Variables with Independent Binary Digits", type = "Report", number = "??", institution = inst-BOEING-SRL, address = inst-BOEING-SRL:adr, pages = "15", month = jan, year = "1970", bibdate = "Wed Nov 12 07:42:28 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.dtic.mil/docs/citations/AD0705642", abstract = "Let $ X = .b_1 b_2 b_3 \ldots {} $ be a random variable with independent binary digits $ b_n $ taking values $0$ or $1$ with probabilities $ p_n$ and $ q_n$. When does $X$ have a density function? A continuous density function? A singular distribution? This note proves that the distribution $X$ is singular is and only if the tail of the series $ \sum (\log (p_n / q_n))$ squared diverges, and that $X$ has a density that is positive on some interval if and only if $ \log (p_n / q_n)$ is a geometric sequence with ratio $ 1 / 2$ for $n$ greater than some $k$, and in that case the fractional part of $ 2^k X$ has an exponential density (increasing or decreasing with the uniform density a special case). It gives a sufficient condition for $X$ to have a density, ($ \sum \log (2 \max (p_n, q_n))$ converges), but unless the tail of the sequence $ \log (p_n / q_n)$ is geometric, ratio $ 1 / 2$, the density is a weird one that vanishes at least once in every interval.", acknowledgement = ack-nhfb, } @Book{McShane:1970:RSE, author = "P. McShane", title = "Randomness, Statistics and Emergence", publisher = "University of Notre Dame Press", address = "South Bend, IN, USA", pages = "x + 268", year = "1970", LCCN = "????", bibdate = "Thu Jan 19 07:09:48 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, remark = "Also published by Gill and Macmillan, Dublin, Ireland.", } @Article{Murry:1970:GAG, author = "Herschell F. Murry", title = "A General Approach for Generating Natural Random Variables", journal = j-IEEE-TRANS-COMPUT, volume = "C-19", number = "12", pages = "1210--1213", month = dec, year = "1970", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1970.222860", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 08:01:39 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671453", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", keywords = "true random numbers from physical sources", } @Article{Payne:1970:FTP, author = "W. H. Payne", title = "{Fortran Tausworthe} pseudorandom number generator", journal = j-CACM, volume = "13", number = "1", pages = "57--57", month = jan, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Washington State Univ. Pullman, WA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "random number generation", } @Article{Prasad:1970:PDA, author = "Ram D. Prasad", title = "Probability Distributions of Algebraic Functions of Independent Random Variables", journal = j-SIAM-J-APPL-MATH, volume = "18", number = "3", pages = "614--626", month = may, year = "1970", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Article{Rader:1970:FMG, author = "C. M. Rader and L. R. Rabiner and R. W. Schafer", title = "A Fast Method of Generating Digital Random Numbers", journal = j-BELL-SYST-TECH-J, volume = "49", number = "9", pages = "2303--2310", month = nov, year = "1970", CODEN = "BSTJAN", ISSN = "0005-8580", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4909.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-9-2303.pdf", abstract = "In this article we propose a fast, efficient technique for generating a pseudorandom stream of uniformly-distributed numbers. The arithmetic operations required are an $L$-bit exclusive-{\em or}, a rotation, and a shift to update the state of the number generator. With moderately large values of $L$ we have been able to generate sequences of numbers whose periods are quite long (on the order of $ 2 \times 10^7 $ long). Its simplicity of construction, as well as its ability to generate long streams of independent pseudorandom uniformly-distributed integers makes this noise generator a worthy candidate for use in high-speed digital systems.", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", remark = "From the paper: ``the maximum period of any random number generator using only flip-flops and exclusive-{\em or} elements \ldots{} is in general $ (2^{2 L} - 1) $. \ldots{} There exist unreasonable starting states, \ldots{}, which have much shorter periods than those described, but these can be avoid in all cases by restricting the starting values to $0$ and $1$. \ldots{} For ($ L = $ ) 25 bits, the longest period results, and is 17,825,775. However, since $ 2^{25} $ is about $ 3.3 \times 10^7 $, not all the possible 25-bit numbers appear at the output of the generator.''", } @Article{Reader:1970:RDM, author = "A. V. Reader", title = "Random digits by a mincing process", journal = j-COMP-J, volume = "13", number = "1", pages = "118--118", month = feb, year = "1970", CODEN = "CMPJA6", DOI = "https://doi.org/10.1093/comjnl/13.1.118", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Tue Dec 4 14:47:44 MST 2012", bibsource = "http://comjnl.oxfordjournals.org/content/13/1.toc; https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_01/", URL = "http://comjnl.oxfordjournals.org/content/13/1/118.full.pdf+html; http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_01/130118.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_01/tiff/118.tif", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Univ. Manchester, UK", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "random number generation", } @Article{Schaffer:1970:AAG, author = "H. E. Schaffer", title = "{ACM Algorithm 369}: Generator of Random Numbers Satisfying the {Poisson} Distribution", journal = j-CACM, volume = "13", number = "1", pages = "49--49", month = jan, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Tue Mar 25 13:26:09 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "North Carolina State Univ., Raleigh, NC, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "random number generation; subroutines", } @Article{Schmidt:1970:QMR, author = "H. Schmidt", title = "Quantum-Mechanical Random-Number Generator", journal = j-J-APPL-PHYS, volume = "41", number = "2", pages = "462--468", day = "1", month = feb, year = "1970", CODEN = "JAPIAU", DOI = "https://doi.org/10.1063/1.1658698", ISSN = "0021-8979 (print), 1089-7550 (electronic), 1520-8850", ISSN-L = "0021-8979", bibdate = "Mon Feb 20 15:46:54 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Physics", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4915369", keywords = "true random numbers from physical sources", } @Article{Schnorr:1970:DEZa, author = "Claus-Peter Schnorr", title = "{{\"U}ber die Definition von effektiven Zufallstests. Teil I}. ({German}) [{On} the definition of effective random tests. {Part I}]", journal = j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB, volume = "15", number = "4", pages = "297--312", month = "????", year = "1970", CODEN = "ZWVGAA", DOI = "https://doi.org/10.1007/BF00533301", ISSN = "0044-3719", ISSN-L = "0044-3719", MRclass = "60.02", MRnumber = "0288794 (44 \#5990a)", bibdate = "Sat Apr 26 19:23:38 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib", URL = "http://link.springer.com/article/10.1007/BF00533301", acknowledgement = ack-nhfb, fjournal = "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete", journal-URL = "http://link.springer.com/journal/440", language = "German", } @Article{Schnorr:1970:DEZb, author = "Claus-Peter Schnorr", title = "{{\"U}ber die Definition von effektiven Zufallstests. Teil II}. ({German}) [{On} the definition of effective random tests. {Part II}]", journal = j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB, volume = "15", number = "4", pages = "313--328", month = "????", year = "1970", CODEN = "ZWVGAA", DOI = "https://doi.org/10.1007/BF00533302", ISSN = "0044-3719", ISSN-L = "0044-3719", MRclass = "60.02", MRnumber = "0288794 (44 \#5990a)", bibdate = "Sat Apr 26 19:23:38 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib", URL = "http://link.springer.com/article/10.1007/BF00533302", acknowledgement = ack-nhfb, fjournal = "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete", journal-URL = "http://link.springer.com/journal/440", language = "German", } @Manual{Smith:1970:RN, author = "Robert E. (Robert Elijah) Smith", title = "Random numbers", organization = "Control Data Corp.", address = "Minneapolis, MN, USA", pages = "82", year = "1970", bibdate = "Sat Jan 27 13:40:57 MST 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Computer explorer series in FORTRAN and BASIC", acknowledgement = ack-nhfb, keywords = "Computer science --- Mathematics.; Number concept.; Programming languages (Electronic computers)", } @Article{Springer:1970:DPB, author = "M. D. Springer and W. E. Thompson", title = "The Distribution of Products of Beta, Gamma and {Gaussian} Random Variables", journal = j-SIAM-J-APPL-MATH, volume = "18", number = "4", pages = "721--737", month = jun, year = "1970", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Article{Stoneham:1970:NCM, author = "R. G. Stoneham", title = "On a New Class of Multiplicative Pseudo-Random Number Generators", journal = j-BIT, volume = "10", number = "4", pages = "481--500", month = dec, year = "1970", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01935568", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Wed Jan 4 18:52:11 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=10&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=4&spage=481", acknowledgement = ack-nhfb, fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", } @Article{Subrahmaniam:1970:SAM, author = "K. Subrahmaniam", title = "On Some Applications of {Mellin} Transforms to Statistics: Dependent Random Variables", journal = j-SIAM-J-APPL-MATH, volume = "19", number = "4", pages = "658--662", month = dec, year = "1970", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Article{Vincent:1970:CGT, author = "C. H. Vincent", title = "Corrigendum: {The Generation of Truly Random Binary Numbers}", journal = j-J-PHYS-E, volume = "3", number = "10", pages = "832--832", month = oct, year = "1970", CODEN = "JPSIAE", DOI = "https://doi.org/10.1088/0022-3735/3/10/528", ISSN = "0022-3735", bibdate = "Sat Nov 29 15:15:40 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Vincent:1970:GTR}.", URL = "http://iopscience.iop.org/0022-3735/3/10/528/", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. E: Scientific instruments", journal-URL = "http://iopscience.iop.org/0022-3735/", } @Article{Vincent:1970:GTR, author = "C. H. Vincent", title = "The Generation of Truly Random Binary Numbers", journal = j-J-PHYS-E, volume = "3", number = "8", pages = "594--598", month = aug, year = "1970", CODEN = "JPSIAE", DOI = "https://doi.org/10.1088/0022-3735/3/8/303", ISSN = "0022-3735", bibdate = "Sat Nov 29 13:56:04 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See corrigendum \cite{Vincent:1970:CGT}.", URL = "http://iopscience.iop.org/0022-3735/3/8/303", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. E: Scientific instruments", journal-URL = "http://iopscience.iop.org/0022-3735/", keywords = "true random numbers from physical sources", } @Article{White:1970:FDC, author = "R. C. {White, Jr.}", title = "A Fast Digital Computer Method for Recursive Estimation of the Mean", journal = j-IEEE-TRANS-COMPUT, volume = "C-19", number = "9", pages = "847--850", month = sep, year = "1970", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1970.223053", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 08:01:36 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See comments \cite{Majithia:1972:CFD}.", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671646", abstract = "An improvement in a method for recursive estimation of the mean of a random variable is suggested. The proposed algorithm is faster than conventional `ideal' averaging and only slightly less efficient, i.e., the estimate variance is only slightly larger for the same sample size.", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Zaremba:1970:DII, author = "S. K. Zaremba", title = "La discr{\'e}pance isotrope et l'int{\'e}gration num{\'e}rique. ({French}) [{Isotropic} discrepancy and numerical integration]", journal = j-ANN-MAT-PURA-APPL-4, volume = "87", number = "??", pages = "125--136", month = "????", year = "1970", CODEN = "ANLMAE", ISSN = "0373-3114 (print), 1618-1891 (electronic)", bibdate = "Thu Jan 19 08:40:01 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Annali di matematica pura ed applicata. Series 4", language = "French", } @Article{Ashford:1971:BRG, author = "J. R. Ashford", title = "Book Reviews: {{\em The Generation of Random Variates}}, by {T. G. Newman} and {P. L. Odell}", journal = j-APPL-STAT, volume = "20", number = "3", pages = "325--325", year = "1971", CODEN = "APSTAG", ISSN = "0035-9254 (print), 1467-9876 (electronic)", ISSN-L = "0035-9254", bibdate = "Sat Apr 21 10:20:12 MDT 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Applied Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues", } @TechReport{Berman:1971:GGD, author = "M. B. Berman", title = "Generating Gamma Distributed Variates for Computer Simulation Models", type = "Report", number = "??", institution = "RAND Corporation", address = "Santa Monica, CA, USA", pages = "??", year = "1971", bibdate = "Tue Nov 29 06:55:32 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Beyer:1971:LSM, author = "W. A. Beyer and R. B. Roof and Dorothy Williamson", title = "The Lattice Structure of Multiplicative Congruential Pseudo-Random Vectors", journal = j-MATH-COMPUT, volume = "25", number = "114", pages = "345--363", month = apr, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", note = "See corrigenda \cite{Beyer:1996:CLS}.", URL = "http://www.jstor.org/stable/pdfplus/2004931.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", remark = "This article, and \cite{Marsaglia:1972:SLC}, are believed to be the first reports of the lattice tests for randomness.", } @Article{Brown:1971:LRA, author = "J. L. {Brown, Jr.} and R. L. Duncan", title = "The Least Remainder Algorithm", journal = j-FIB-QUART, volume = "9", number = "4", pages = "347--350", month = oct, year = "1971", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:39 MDT 2011", bibsource = "http://www.fq.math.ca/9-4.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.fq.math.ca/Scanned/9-4/brown-a.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Chen:1971:RNN, author = "Edwin H. Chen", title = "A random normal number generator for 32-bit-word computers", journal = j-J-AM-STAT-ASSOC, volume = "66", number = "334", pages = "400--403", month = jun, year = "1971", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Thu Dec 22 07:42:23 2011", bibsource = "Distributed/QLD.bib; Distributed/QLD/1971.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2283944", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG", enum = "7123", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", location = "SEL: Wi", revision = "16/01/94", } @Article{Cohn:1971:PRB, author = "Charles Erwin Cohn", title = "The performance of random-bit generators", journal = j-SIMULATION, volume = "17", number = "6", pages = "234--236", month = dec, year = "1971", CODEN = "SIMUA2", DOI = "https://doi.org/10.1177/003754977101700604", ISSN = "0037-5497 (print), 1741-3133 (electronic)", ISSN-L = "0037-5497", bibdate = "Wed Jan 11 11:59:19 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://sim.sagepub.com/content/17/6/234.full.pdf+html", acknowledgement = ack-nhfb, fjournal = "Simulation", journal-URL = "http://sim.sagepub.com/content/by/year", remark = "Discusses three physical-device random bit generators and shows that all have significant bias.", } @Article{Craddock:1971:TRM, author = "J. M. Craddock and Sheila A. Farmer", title = "Two Robust Methods of Random Number Generation", journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN, volume = "20", number = "3", pages = "55--66", month = sep, year = "1971", CODEN = "????", ISSN = "0039-0526 (print), 1467-9884 (electronic)", ISSN-L = "0039-0526", bibdate = "Wed Dec 21 09:52:10 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2986798", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series D (The Statistician)", journal-URL = "http://www.jstor.org/journals/00390526.html", } @Article{Davies:1971:PWO, author = "A. C. Davies", title = "Properties of Waveforms Obtained by Nonrecursive Digital Filtering of Pseudorandom Binary Sequences", journal = j-IEEE-TRANS-COMPUT, volume = "C-20", number = "3", pages = "270--281", month = mar, year = "1971", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1971.223231", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Wed Jul 13 06:38:13 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671824", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Dieter:1971:EDS, author = "Ulrich Dieter and J. Ahrens", title = "An exact determination of serial correlations of pseudo-random numbers", journal = j-NUM-MATH, volume = "17", number = "2", pages = "101--123", month = apr, year = "1971", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "Distributed/QLD.bib; Distributed/QLD/1971.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classification = "C7890 (Other special applications of computing)", corpsource = "Univ. Karlsruhe, West Germany", country = "D", date = "00/00/00", descriptors = "RNG; correlation", enum = "777", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "linear congruential methods; random number generation; serial correlations", location = "PKI-OG: Li-Ord.Le", references = "0", revision = "21/04/91", treatment = "T Theoretical or Mathematical", } @Article{Dieter:1971:PRN, author = "Ulrich Dieter", title = "Pseudo-Random Numbers: The Exact Distribution of Pairs", journal = j-MATH-COMPUT, volume = "25", number = "116", pages = "855--883", month = oct, year = "1971", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Donn:1971:MDP, author = "E. S. Donn", title = "Manipulating digital patterns with a new binary sequence generator", journal = j-HEWLETT-PACKARD-J, volume = "22", number = "8", pages = "2--8", month = apr, year = "1971", CODEN = "HPJOAX", ISSN = "0018-1153", bibdate = "Tue Mar 25 14:12:15 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "B7250E (Signal generators)", fjournal = "Hewlett-Packard Journal: technical information from the laboratories of Hewlett-Packard Company", keywords = "digital instrumentation; digital pattern manipulation; pseudorandom binary sequence generator; sequence generating; shift register", treatment = "N New Development", } @InProceedings{Dyadkin:1971:ANA, author = "I. G. Dyadkin", booktitle = "{Monte Carlo} methods and applications ({Metody Monte-Karlo i ikh primeneniya USSR Academy of Sciences, Siberian Branch. Computing Center (VTs SO AN SSSR). Novosibirsk, 30 August--3 September 1971 (Vychislitelnyi Tsentr, Sibirskoye Otdelenie. Akademiia Nauk. SSSR)})", title = "An analogue of {von Neumann}'s algorithm for simulating a normal distribution", publisher = "Akademiia Nauk SSSR", address = "Novosibirsk, USSR", pages = "53--54", year = "1971", bibdate = "Mon Feb 27 09:50:56 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "Russian", } @Article{Friedman:1971:REG, author = "Jerome H. Friedman", title = "Random event generation with preferred frequency distributions", journal = j-J-COMPUT-PHYS, volume = "7", number = "2", pages = "201--218", month = apr, year = "1971", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(71)90085-4", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Sun Jan 1 09:15:03 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.sciencedirect.com/science/article/pii/0021999171900854", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", } @Book{Gibbons:1971:NSI, author = "Jean Dickinson Gibbons", title = "Nonparametric Statistical Inference", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xiv + 306", year = "1971", ISBN = "0-07-085250-2, 0-07-023166-4", ISBN-13 = "978-0-07-085250-1, 978-0-07-023166-5", LCCN = "QA278.8 .G5", bibdate = "Tue Jan 31 14:57:32 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "McGraw-Hill series in probability and statistics", acknowledgement = ack-nhfb, } @InProceedings{Good:1971:SRS, author = "I. J. Good and R. A. Gaskins", editor = "A. O. L. (Arthur O. L.) Atkin and B. J. (Bryan John) Birch", booktitle = "{Computers in number theory: proceedings of the Science Research Council Atlas Symposium no. 2 held at Oxford, from 18--23 August, 1969}", title = "Some relationships satisfied by additive and multiplicative congruential sequences, with implications for pseudorandom number generation", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, bookpages = "xvii + 433", pages = "125--136", year = "1971", ISBN = "0-12-065750-3", ISBN-13 = "978-0-12-065750-6", LCCN = "QA241 .S35 1969", bibdate = "Sat Jan 07 08:00:00 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, meetingname = "Science Research Council Atlas Symposium, 2d, Oxford, 1969.", subject = "Number theory; Data processing; Congresses", } @Article{Han:1971:DRV, author = "Chien-Pai Han", title = "Dependence of Random Variables", journal = j-AMER-STAT, volume = "25", number = "4", pages = "35--35", month = oct, year = "1971", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 10:52:19 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326371; https://www.math.utah.edu/pub/tex/bib/amstat1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2682925", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Jackson:1971:PCC, author = "P. A. Jackson", title = "{PRBS} cross-correlation measurements by hybrid computational techniques", journal = j-COMP-J, volume = "14", number = "1", pages = "49--54", month = feb, year = "1971", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Fri Sep 29 08:51:51 MDT 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/compj1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/140049.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/tiff/49.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/tiff/50.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/tiff/51.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/tiff/52.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/tiff/53.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_01/tiff/54.tif", acknowledgement = ack-nhfb, classcodes = "C1220 (Simulation, modelling and identification); C5460 (Analogue and hybrid computing techniques)", corpsource = "Lanchester Coll. Technol., Coventry, UK", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "binary sequences; correlation methods; cross correlation; dynamics identification; hybrid computational techniques; hybrid computer; identification; methods; pseudorandom binary sequence; system", treatment = "T Theoretical or Mathematical", } @Article{Kozlov:1971:DRN, author = "G. A. Kozlov", title = "On the Distribution of Random Numbers Produced by Sequential Physical Generators", journal = j-THEORY-PROBAB-APPL, volume = "16", number = "2", pages = "369--378", month = "????", year = "1971", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/1116037", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Tue Apr 1 10:36:25 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/16/2; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", onlinedate = "January 1971", } @Article{Marsaglia:1971:RVI, author = "George Marsaglia", title = "Random variables with independent binary digits", journal = j-ANN-MATH-STAT, volume = "42", number = "6", pages = "1922--1929", month = dec, year = "1971", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177693058", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "60A05", MRnumber = "45 \#7764", MRreviewer = "A. Fuchs", bibdate = "Fri Jan 6 09:58:57 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", URL = "http://projecteuclid.org/euclid.aoms/1177693058; http://www.jstor.org/stable/2240118", ZMnumber = "0239.60015", abstract = "Let $ X = \cdot b_1 b_2 b_3 \cdots $ be a random variable with independent binary digits $ b_n $ taking values 0 or 1 with probability $ p_n $ and $ q_n = 1 - p_n $. When does $X$ have a density? A continuous density? A singular distribution? This note gives necessary and sufficient conditions for the distribution of $X$ to be: discrete: $ \Sigma \min (p_n, q_n) < \infty $; singular: $ \Sigma^\infty_m \lbrack \log (p_n / q_n) \rbrack^2 = \infty $ for every $m$; absolutely continuous: $ \Sigma^\infty_m \lbrack \log (p_n / q_n) \rbrack^2 < \infty $ for some $m$. Furthermore, $X$ has a density that is bounded away from zero on some interval if and only if $ \log (p_n / q_n) $ is a geometric sequence with ratio $ \frac {1}{2} $ for $ n > k $, and in that case the fractional part of $ 2^k X $ has an exponential density (increasing or decreasing with the uniform a special case).", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", ZMclass = "60E05 General theory of probability distributions 60F99 Limit theorems (probability)", } @Article{Mitra:1971:PDS, author = "Samarendra Kumar Mitra", title = "On the Probability Distribution of the Sum of Uniformly Distributed Random Variables", journal = j-SIAM-J-APPL-MATH, volume = "20", number = "2", pages = "195--198", month = mar, year = "1971", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Book{Newman:1971:GRVa, author = "Thomas G. Newman and Patrick L. Odell", title = "The generation of random variates", volume = "29", publisher = "Charles Griffin \& Co. Ltd.", address = "London, UK", pages = "viii + 88", year = "1971", ISBN = "0-85264-194-X", ISBN-13 = "978-0-85264-194-1", LCCN = "QA276.5 N55", bibdate = "Thu Jan 19 07:23:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Griffin's Statistical Monographs and Courses", acknowledgement = ack-nhfb, } @Book{Newman:1971:GRVb, author = "Thomas G. Newman and Patrick L. Odell", title = "The generation of random variates", publisher = "Hafner", address = "New York, NY, USA", pages = "88 (est.)", year = "1971", ISBN = "????", ISBN-13 = "????", LCCN = "QA276.5 N55", bibdate = "Thu Jan 19 07:23:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @InProceedings{Payne:1971:CDS, author = "W. H. Payne and T. G. Lewis", title = "Continuous distribution sampling: accuracy and speed", crossref = "Rice:1971:MS", pages = "??--??", year = "1971", bibdate = "Mon Jan 16 22:01:09 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Book{Philipp:1971:MSR, author = "Walter Philipp", title = "Mixing sequences of random variables and probablistic number theory", volume = "114", publisher = pub-AMS, address = pub-AMS:adr, pages = "i + 102", year = "1971", LCCN = "????", MRclass = "10K10 (10KXX 60F05 60F15)", MRnumber = "0437481 (55 \#10411)", MRreviewer = "J. Galambos", bibdate = "Thu Jan 19 08:03:34 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "Memoirs of the American Mathematical Society", acknowledgement = ack-nhfb, } @InProceedings{Phillips:1971:PGG, author = "Don T. Phillips and Charles Beightler", booktitle = "Proceedings of the 5th Conference on Winter Simulation --- {WSC '71}", title = "Procedures for generating gamma variates with non-integer parameter sets", publisher = pub-ACM, address = pub-ACM:adr, pages = "421--427", year = "1971", DOI = "https://doi.org/10.1145/800294.811468", bibdate = "Tue Nov 29 08:26:27 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Rizzi:1971:MGS, author = "Alfredo Rizzi", title = "On a method for generating sequences of binary pseudo random numbers", journal = j-METRON, volume = "29", number = "??", pages = "61--70", month = "????", year = "1971", CODEN = "MRONAM", ISSN = "0026-1424 (print), 2281-695X (electronic)", ISSN-L = "0026-1424", MRclass = "65C10", bibdate = "Sun Jul 5 08:55:46 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/metron1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0233.65004", acknowledgement = ack-nhfb, xxyear = "1972", ZMnumber = "03369649", } @Article{Schnorr:1971:UAD, author = "Claus-Peter Schnorr", title = "A unified approach to the definition of random sequences", journal = j-THEORY-COMPUT-SYST, volume = "5", number = "3", pages = "246--258", month = sep, year = "1971", CODEN = "TCSYFI", DOI = "https://doi.org/10.1007/BF01694181", ISSN = "1432-4350 (print), 1433-0490 (electronic)", bibdate = "Tue Jan 17 10:27:01 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.springerlink.com/content/u08164t2503054rk/", acknowledgement = ack-nhfb, fjournal = "Theory of Computing Systems", } @Book{Schnorr:1971:ZWA, author = "Claus Peter Schnorr", title = "{Zuf{\"a}lligkeit} und Wahrscheinlichkeit: Eine algorithmische {Begr{\"u}ndung} der Wahrscheinlichkeitstheorie. ({German}) [{Randomness} and probability. {An} algorithmic foundation of probability theory]", volume = "218", publisher = pub-SV, address = pub-SV:adr, pages = "iv + 212", year = "1971", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0112458", ISBN = "3-540-05566-5 (print), 3-540-36883-3 (e-book)", ISBN-13 = "978-3-540-05566-2 (print), 978-3-540-36883-0 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", bibdate = "Tue May 6 14:51:37 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/lnm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", series = ser-LECT-NOTES-MATH, URL = "http://link.springer.com/book/10.1007/BFb0112458; http://www.springerlink.com/content/978-3-540-36883-0", acknowledgement = ack-nhfb, language = "German", series-URL = "http://link.springer.com/bookseries/304", } @Article{Smith:1971:MPR, author = "C. S. Smith", title = "Multiplicative Pseudo-Random Number Generators with Prime Modulus", journal = j-J-ACM, volume = "18", number = "4", pages = "586--593", month = oct, year = "1971", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321662.321673", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Sun Nov 6 12:03:57 1994", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @TechReport{Strawderman:1971:GTP, author = "W. E. Strawderman", title = "Generation and testing of pseudo-random numbers", type = "Technical Report", number = "171", institution = "Department of Statistics, Stanford University", address = "Stanford, CA, USA", month = "????", year = "1971", bibdate = "Wed Nov 12 09:41:24 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Book{Stroud:1971:ACM, author = "A. H. Stroud", title = "Approximate calculation of multiple integrals", publisher = pub-PH, address = pub-PH:adr, pages = "xiii + 431", year = "1971", ISBN = "0-13-043893-6", ISBN-13 = "978-0-13-043893-5", LCCN = "QA311 .S85", bibdate = "Mon Jan 16 11:19:32 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "Prentice-Hall series in automatic computation", acknowledgement = ack-nhfb, subject = "multiple integrals; approximation theory; Monte Carlo quadrature", } @Article{Tootill:1971:RPT, author = "J. P. R. Tootill and W. D. Robinson and A. G. Adams", title = "The Runs Up-and-Down Performance of {Tausworthe} Pseudo-Random Number Generators", journal = j-J-ACM, volume = "18", number = "3", pages = "381--399", month = jul, year = "1971", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321650.321657", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Thu Dec 22 07:42:23 2011", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1971.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, annote = "Any Tausworthe generator based upon a primitive trinomial over $ g f(2), x^p + x^q + 1 $, can be represented as a simple linear recurrence in $ g f(2^p) $. For a generator producing a sequence of $p$-bit pseudorandom numbers, $ (p, 2^p - 1) = 1 $, which is guaranteed by Tausworthe's theory to be 1-distributed, the recurrence may reveal combinatorial relationships implying a poor runs up-and-down performance. This occurs when $q$ is small, too near $ p / 2 $, or nearly \ldots{}", descriptors = "Tausworthe generator; shift register sequences; rng; test; runtime/storage efficiency", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Vincent:1971:PAG, author = "C. H. Vincent", title = "Precautions for accuracy in the generation of truly random binary numbers", journal = j-J-PHYS-E, volume = "4", number = "11", pages = "825--828", month = "????", year = "1971", CODEN = "JPSIAE", DOI = "https://doi.org/10.1088/0022-3735/4/11/007", ISSN = "0022-3735", bibdate = "Thu Feb 02 17:58:43 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See corrigendum \cite{Vincent:1972:CPA}.", URL = "http://iopscience.iop.org/0022-3735/4/11/007", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. E: Scientific instruments", journal-URL = "http://iopscience.iop.org/0022-3735/", keywords = "true random numbers from physical sources", } @Article{Voroncov:1971:UQS, author = "Ju. V. Voroncov and Ju. G. Polljak", title = "On the use of quasirandom sequences in the direct probabilistic simulation of systems", journal = "Avtomat. i Vy\v cisl. Tehn.", volume = "6", number = "??", pages = "23--27", month = "????", year = "1971", CODEN = "????", ISSN = "????", bibdate = "Thu Jan 19 08:29:53 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Avt. i Vy{\v{c}}isl. Tehn.", fjournal = "Akademija Nauk Latvi\u\i sko\u\i\ SSR. Avtomatika i Vy\v cislitel\cprime naja Tehnika", language = "Russian", } @Article{Zinger:1971:LLC, author = "A. A. Zinger", title = "Limit laws for cumulative sums of independent random variables with a finite number of distribution types", journal = j-THEORY-PROBAB-APPL, volume = "16", number = "??", pages = "596--619", month = "????", year = "1971", CODEN = "TPRBAU", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Mon Dec 07 17:39:39 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib", note = "Original Russian article in {\em Teor. Veroyatnost. i Primenen.}, {\bf 16}, (1971), pp. 614--637.", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", } @Article{Ahrens:1972:CMS, author = "Joachim H. Ahrens and Ulrich Dieter", title = "Computer Methods for Sampling from the Exponential and Normal Distributions", journal = j-CACM, volume = "15", number = "10", pages = "873--882", month = oct, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65C10", MRnumber = "49 1728", MRreviewer = "V. Dupac", bibdate = "Mon Jan 22 06:20:51 MST 2001", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1972.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#AhrensD72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "Various methods are known for transforming uniformly distributed random numbers into exponentially and normally distributed quantities. The most efficient ones are compared, in terms of memory requirements and speed, with some new algorithms. A number of procedures convert Taylor series expansions directly into sampling steps, an approach which may be used for sampling from any continuous distribution. For the exponential distribution a definite recommendation can be made, whereas in the case of the normal distribution there remains a choice between slower and shorter algorithms and faster but space consuming methods.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", classification = "913; 922", corpsource = "Nova Scotia Tech. Coll., Halifax, NS, Canada", country = "USA", descriptors = "RVG", enum = "6926", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", journalabr = "Commun ACM", keywords = "computer aided sampling; computer methods; distributed random numbers; distributions; exponential; normal distributions; random number generation; sampled data systems; sampling; sampling steps; uniformly", oldlabel = "AhrensD72", references = "0", treatment = "T Theoretical or Mathematical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/AhrensD72", } @Article{Alam:1972:AVM, author = "Khursheed Alam", title = "Asymptotic Value of the Mean of a Function of a Normal Random Variable", journal = j-SIAM-J-APPL-MATH, volume = "23", number = "4", pages = "495--498", month = dec, year = "1972", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Article{Barr:1972:CMN, author = "Donald R. Barr and Norman L. Sezak", title = "A Comparison of Multivariate Normal Generators", journal = j-CACM, volume = "15", number = "12", pages = "1048--1049", month = dec, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 06:23:32 MST 2001", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#BarrS72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Naval Postgraduate School, Monterey, CA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "comparison; covariance matrix; Gaussian random number generator; multivariate; multivariate normal generators; normal random vectors; random number generation; simulation; triangular factorization", oldlabel = "BarrS72", treatment = "T Theoretical or Mathematical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BarrS72", } @Article{Basu:1972:ITF, author = "A. K. Basu", title = "Invariance theorems for first passage time random variables", journal = j-CAN-MATH-BULL, volume = "15", number = "??", pages = "171--176", month = "????", year = "1972", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/CMB-1972-031-9", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", bibdate = "Thu Sep 8 10:04:00 MDT 2011", bibsource = "http://cms.math.ca/cmb/v15/; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Canadian mathematical bulletin = Bulletin canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cmb/", } @Article{Behboodian:1972:CNS, author = "Javad Behboodian", title = "Classroom Notes: a Simple Example on Some Properties of Normal Random Variables", journal = j-AMER-MATH-MONTHLY, volume = "79", number = "6", pages = "632--634", month = jun # "\slash " # jul, year = "1972", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:47 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @InProceedings{Beyer:1972:LSR, author = "W. A. Beyer", title = "Lattice structure and reduced bases of random vectors generated by linear recurrences", crossref = "Zaremba:1972:ANT", pages = "361--370", year = "1972", bibdate = "Tue Jan 10 15:36:07 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Broemeling:1972:BPD, author = "L. D. Broemeling", title = "{Bayesian} procedures for detecting a change in a sequence of random variables", journal = j-METRON, volume = "30", number = "??", pages = "214--227", month = "????", year = "1972", CODEN = "MRONAM", ISSN = "0026-1424 (print), 2281-695X (electronic)", ISSN-L = "0026-1424", MRclass = "62F15 62C10 62F03", bibdate = "Sun Jul 5 08:55:46 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/metron1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0303.62029", acknowledgement = ack-nhfb, xxyear = "1973", ZMnumber = "03474769", } @Article{Cenacchi:1972:QRS, author = "G. Cenacchi and A. {De Matteis}", title = "Quasi-random sequences by power residues", journal = j-NUM-MATH, volume = "20", number = "1", pages = "54--63", month = feb, year = "1972", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon Oct 18 01:28:20 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/nummath.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Chang:1972:FSD, author = "R. W. Chang and E. Y. Ho", title = "On Fast Start-Up Data Communication Systems Using Pseudo-Random Training Sequences", journal = j-BELL-SYST-TECH-J, volume = "51", number = "9", pages = "2013--2027", month = nov, year = "1972", CODEN = "BSTJAN", ISSN = "0005-8580", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1972/BSTJ.1972.5109.html; http://www.alcatel-lucent.com/bstj/vol51-1972/bstj-vol51-issue09.html; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol51/bstj51-9-2013.pdf; http://www.alcatel-lucent.com/bstj/vol51-1972/articles/bstj51-9-2013.pdf", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @InCollection{Dieter:1972:SIP, author = "U. Dieter", title = "Statistical interdependence of pseudo-random numbers generated by the linear congruential method", crossref = "Zaremba:1972:ANT", pages = "287--317", year = "1972", MRnumber = "MR 353622", bibdate = "Thu Jan 19 06:38:32 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Elias:1972:ECU, author = "P. Elias", title = "The efficient construction of an unbiased random sequence", journal = j-ANN-MATH-STAT, volume = "43", number = "3", pages = "865--870", month = jun, year = "1972", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Tue Jan 31 15:45:16 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2240383", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", } @Article{Ermakov:1972:NPSa, author = "S. M. Ermakov", title = "Note on pseudorandom sequences", journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.", volume = "12", number = "??", pages = "??--??", month = "????", year = "1972", ISSN = "1077-1082", bibdate = "Thu Jan 19 06:40:29 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "Zbl 0294.65003", acknowledgement = ack-nhfb, language = "Russian", } @Article{Ermakov:1972:NPSb, author = "S. M. Ermakov", title = "Note on pseudorandom sequences", journal = j-USSR-COMP-MATH-MATH-PHYS, volume = "12", number = "4", pages = "307--314", month = "????", year = "1972", CODEN = "CMMPA9", DOI = "https://doi.org/10.1016/0041-5553(72)90136-X", ISSN = "0041-5553, 0502-9902", ISSN-L = "0041-5553", MRnumber = "MR 329191", bibdate = "Thu Jan 19 06:42:16 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.sciencedirect.com/science/article/pii/004155537290136X", abstract = "A sequence $ x_{n + 1} = \{ M x_n \} $, $ x_0 (0, 1) $ is considered, where $ \{ a \} $ denotes the fractional part of the number $a$ and $ M > 1 $ is a natural number. It is shown that when this sequence is used as a pseudorandom sequence in calculations by the Monte-Carlo method, the central limit theorem holds for a fairly wide class of the functions integrated.", acknowledgement = ack-nhfb, fjournal = "U.S.S.R. Computational Mathematics and Mathematical Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00415553", } @TechReport{Everett:1972:MCS, author = "C. J. Everett and E. D. Cashwell", title = "A {Monte Carlo} Sampler", type = "Informal Report", number = "LA-5061-MS", institution = inst-LASL, address = inst-LASL:adr, year = "1972", bibdate = "Mon Jan 16 10:57:49 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Falk:1972:EDT, author = "H. Falk", title = "Entropy Decomposition and Transfer-Matrix Problems", journal = j-J-MATH-PHYS, volume = "13", number = "5", pages = "608--609", month = may, year = "1972", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.1666023", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Fri Oct 28 16:39:49 MDT 2011", bibsource = "http://jmp.aip.org/; https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://jmp.aip.org/resource/1/jmapaq/v13/i5/p608_s1", acknowledgement = ack-nhfb, classification = "A0520 (Statistical mechanics)", corpsource = "City Univ., NY, USA", fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", keywords = "discrete random variables; entropy; entropy decomposition; Markovian decomposition; short range interactions; transfer matrix problems", onlinedate = "31 October 2003", pagecount = "2", treatment = "T Theoretical or Mathematical", } @TechReport{Forsythe:1972:NCMa, author = "George E. Forsythe", title = "{Von Neumann}'s comparison method for random sampling from the normal and other distributions", type = "Technical Report", number = "CS-TR-72-254", institution = inst-STAN-CS, address = inst-STAN-CS:adr, pages = "21", month = jan, year = "1972", bibdate = "Mon Jun 06 19:17:03 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Techreports/NCSTRL/STAN.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Techreports/STAN.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Techreports/Stanford.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "The author presents a generalization he worked out in 1950 of von Neumann's method of generating random samples from the exponential distribution by comparisons of uniform random numbers on (0,1). It is shown how to generate samples from any distribution whose probability density function is piecewise both absolutely continuous and monotonic on $ ( - \infty, \infty) $. A special case delivers normal deviates at an average cost of only 4.036 uniform deviates each. This seems more efficient than the Center-Tail method of Dieter and Ahrens, which uses a related, but different, method of generalizing the von Neumann idea to the normal distribution.", acknowledgement = ack-nhfb, notes = "[Adminitrivia V1/Prg/19951016]", } @Article{Forsythe:1972:NCMb, author = "George E. Forsythe", title = "{Von Neumann}'s comparison method for random sampling from the normal and other distributions", journal = j-MATH-COMPUT, volume = "26", number = "120", pages = "817--826", month = oct, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65C10", MRnumber = "MR0315863 (47 \#4412)", MRreviewer = "R. R. Coveyou", bibdate = "Tue Nov 22 09:08:17 MST 2005", bibsource = "Distributed/QLD.bib; Distributed/QLD/1972.bib; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Distributed/QLD/1972.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/mathcomp.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/MATHCOMP/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", ZMnumber = "0283.65003", acknowledgement = ack-nhfb, by-date = "Wi", by-rev = "Le", classcodes = "B0240 (Probability and statistics); C1140 (Probability and statistics)", classmath = "*65C10 Random number generation 62D05 Statistical sampling theory", corpsource = "Stanford Univ., CA, USA", date = "13/05/93", descriptors = "RVG", enum = "7276", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "distribution; normal; random sampling; sampled data systems; statistics; Von Neumann's comparison method", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", treatment = "T Theoretical or Mathematical", } @Article{Frazer:1972:BOM, author = "W. D. Frazer and B. T. Bennett", title = "Bounds on Optimal Merge Performance, and a Strategy for Optimality", journal = j-J-ACM, volume = "19", number = "4", pages = "641--648", month = oct, year = "1972", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321724.321729", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "The length of a sorted sequence produced by the internal sort phase of a large scale general purpose sort routine is a random variable. In a random access environment, any given set of such sequences can be merged in an optimal way, and in practice this often done. the expected work per item required by an optimal merge depends upon the probability distribution for sequence length, and it is this dependence which is studied. Reasonable sharp upper and lower bounds are derived. The distribution which is optimal in the sense of minimizing the lower bound on any bounded interval is determined, and it is shown that this is the strongest result of its kind.", acknowledgement = ack-nhfb, classification = "723", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", journalabr = "J Assoc Comput Mach", keywords = "computer systems programming; data storage, digital --- Random Access", } @Article{Garside:1972:BRBa, author = "M. J. Garside", title = "Book Review: {{\booktitle{The Generation of Random Variates}}, by T. G. Newman; P. L. Odell}", journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN, volume = "21", number = "2", pages = "143--143", month = jun, year = "1972", CODEN = "????", DOI = "https://doi.org/10.2307/2987327", ISSN = "0039-0526 (print), 1467-9884 (electronic)", ISSN-L = "0039-0526", bibdate = "Thu Jan 22 18:10:20 MST 2015", bibsource = "http://www.jstor.org/stable/i349925; https://www.math.utah.edu/pub/tex/bib/jrss-d-1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2987327", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series D (The Statistician)", journal-URL = "http://www.jstor.org/journals/00390526.html", } @Article{Heathcote:1972:TGF, author = "C. E. Heathcote", title = "A Test of Goodness of Fit for Symmetric Random Variables", journal = j-AUST-J-STAT, volume = "14", number = "2", pages = "172--181", month = aug, year = "1972", CODEN = "AUJSA3", DOI = "https://doi.org/10.1111/j.1467-842X.1972.tb00355.x", ISSN = "0004-9581", ISSN-L = "0004-9581", bibdate = "Fri Jul 15 14:28:03 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/anzjs.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Australian Journal of Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues", } @Article{Hurst:1972:AAG, author = "Rex L. Hurst and Robert E. Knop", title = "{ACM Algorithm 425}: Generation of Random Correlated Normal Variables [{G5}]", journal = j-CACM, volume = "15", number = "5", pages = "355--357", month = may, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 06:51:29 MST 2001", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#HurstK72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See remark \cite{Page:1974:RAG}.", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics computing)", corpsource = "Utah State Univ., Logan, UT, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "algorithms; FORTRAN subroutine; generation; multivariate normal density; random correlated normal variables; statistics; subroutines; timing", oldlabel = "HurstK72", treatment = "T Theoretical or Mathematical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HurstK72", } @Article{Kirschenmann:1972:CR, author = "P. Kirschenmann", title = "Concepts of randomness", journal = j-J-PHILOS-LOGIC, volume = "1", number = "??", pages = "395--414", month = "????", year = "1972", CODEN = "JPLGA7", ISSN = "0022-3611 (print), 1573-0433 (electronic)", ISSN-L = "0022-3611", MRnumber = "MR 426081", bibdate = "Mon Jan 16 21:58:56 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Philosophical Logic", } @Article{Kral:1972:ENA, author = "J. Kr{\'a}l", title = "Erratum: {``A new additive pseudorandom number generator for extremely short word-length''}", journal = j-INFO-PROC-LETT, volume = "1", number = "5", pages = "216--216", month = oct, year = "1972", CODEN = "IFPLAT", ISSN = "0020-0190 (print), 1872-6119 (electronic)", ISSN-L = "0020-0190", bibdate = "Tue Nov 17 10:49:43 MST 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Kral:1972:NAP}.", acknowledgement = ack-nhfb, fjournal = "Information Processing Letters", journal-URL = "http://www.sciencedirect.com/science/journal/00200190", } @Article{Kral:1972:NAP, author = "J. Kr{\'a}l", title = "A new additive pseudorandom number generator for extremely short word-length", journal = j-INFO-PROC-LETT, volume = "1", number = "4", pages = "164--167", month = jun, year = "1972", CODEN = "IFPLAT", DOI = "https://doi.org/10.1016/0020-0190(72)90051-8", ISSN = "0020-0190 (print), 1872-6119 (electronic)", ISSN-L = "0020-0190", bibdate = "Tue Nov 17 10:49:43 MST 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See erratum \cite{Kral:1972:ENA}.", abstract = "We study the suitability of the additive lagged-Fibonacci pseudo-random number generator for parallel computation. This generator has relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of full-period cycles it contains. These different full period cycles are called equivalence classes. We show how to enumerate the equivalence classes and how to compute seeds to select a given equivalence class, In addition, we present some theoretical measures of quality for this generator when used in parallel. Next, we conjecture on the size of these measures of quality for this generator. Extensive empirical evidence supports this conjecture. In addition, a probabilistic interpretation of these measures leads to another conjecture similarly supported by empirical evidence. Finally we give an explicit parallelization suitable for a fully reproducible asynchronous MIMD implementation.", acknowledgement = ack-nhfb, classification = "C7890 (Other special applications of computing)", corpsource = "RWTH, Aachen, West Germany", fjournal = "Information Processing Letters", journal-URL = "http://www.sciencedirect.com/science/journal/00200190", keywords = "additive pseudorandom number generator; CDC FORTRAN subroutine; extremely short word lengths; mod 2/sup j/ arithmetics; random number generation; shuffling; subroutines", treatment = "T Theoretical or Mathematical", } @Article{Maddocks:1972:CAG, author = "R. S. Maddocks and S. Matthews and E. W. Walker and C. H. Vincent", title = "A compact and accurate generator for truly random binary digits", journal = j-J-PHYS-E, volume = "5", number = "??", pages = "542--544", month = "????", year = "1972", CODEN = "JPSIAE", ISSN = "0022-3735", bibdate = "Thu Feb 02 17:34:15 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://iopscience.iop.org/0022-3735/5/6/018", acknowledgement = ack-nhfb, fjournal = "Journal of physics. E: Scientific instruments", journal-URL = "http://iopscience.iop.org/0022-3735/", keywords = "true random numbers from physical sources", } @Article{Majithia:1972:CFD, author = "J. C. Majithia", title = "Comments on {``A Fast Digital Computer Method for Recursive Estimation of the Mean''}", journal = j-IEEE-TRANS-COMPUT, volume = "C-21", number = "5", pages = "511--512", month = may, year = "1972", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1972.223554", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Tue Jul 12 18:58:43 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{White:1970:FDC}.", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672147", abstract = "Several algorithms for the computation of the mean value of a random variable have been analyzed. Results have shown that the two previously published techniques and a modified version of one of these, give unbiased estimates of the mean value. Furthermore, although the confidence intervals have been found to be increased in all cases, the actual increase is insignificant, while the possible speed improvements in computation can be considerable.", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Marsaglia:1972:CPS, author = "George Marsaglia", title = "Choosing a point from the surface of a sphere", journal = j-ANN-MATH-STAT, volume = "43", number = "2", pages = "645--646", month = apr, year = "1972", CODEN = "AASTAD", DOI = "https://doi.org/10.1214/aoms/1177692644", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", MRclass = "65C10", bibdate = "Thu Jan 19 08:45:34 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://projecteuclid.org/euclid.aoms/1177692644; http://www.jstor.org/stable/2240001", ZMnumber = "0248.65008", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", ZMclass = "65C10 Random number generation", } @InCollection{Marsaglia:1972:SLC, author = "George Marsaglia", title = "The Structure of Linear Congruential Sequences", crossref = "Zaremba:1972:ANT", pages = "249--285", year = "1972", MRclass = "65C05", MRnumber = "53 \#14854", MRreviewer = "J. H. Halton", bibdate = "Mon Aug 02 10:41:44 2004", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; MathSciNet database", ZMnumber = "0266.65007", acknowledgement = ack-nhfb, remark = "This article, and \cite{Beyer:1971:LSM}, are believed to be the first reports of the lattice tests for randomness.", ZMclass = "65C10 Random number generation", } @Article{Mason:1972:LTN, author = "J. David Mason", title = "Local Theorems for Nonidentically Distributed Lattice Random Variables", journal = j-SIAM-J-APPL-MATH, volume = "22", number = "2", pages = "259--265", month = mar, year = "1972", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, classification = "A0550 (Lattice theory and statistics; Ising problems)", corpsource = "Univ. Georgia, Athens, GA, USA", fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", keywords = "lattice theory and statistics; local theorems; nondegenerate distribution; nonidentically distributed lattice random variables; random processes", treatment = "T Theoretical or Mathematical", } @Article{Meyer:1972:PCC, author = "C. H. Meyer and W. L. Tuchman", title = "Pseudorandom codes can be cracked", journal = j-ELECTRONIC-DESIGN, volume = "20", number = "23", pages = "74--76", day = "9", month = nov, year = "1972", CODEN = "ELODAW", ISSN = "0013-4872 (print), 1944-9550 (electronic)", ISSN-L = "0013-4872", bibdate = "Sat Jun 10 12:07:32 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Electronic Design", } @InBook{Mihram:1972:SV, author = "G. Arthur Mihram", booktitle = "Simulation: Statistical Foundations and Methodology", title = "The Stochastic Variate", chapter = "2", volume = "92", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, bookpages = "xv + 526", pages = "18--146", month = jun, year = "1972", DOI = "https://doi.org/10.1016/S0076-5392(08)61350-8", ISBN = "0-12-495950-4", ISBN-13 = "978-0-12-495950-7", LCCN = "TA343 .M53", bibdate = "Wed Feb 8 07:02:04 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = j-MATH-SCI-ENG, URL = "http://www.sciencedirect.com/science/article/pii/S0076539208613508", acknowledgement = ack-nhfb, fjournal = "Mathematics in Science and Engineering", } @Article{Miyatake:1972:GUR, author = "O. Miyatake", title = "Generation of uniform random numbers of good quality", journal = j-MATH-JAPON, volume = "17", number = "??", pages = "79--84", month = "????", year = "1972", CODEN = "MAJAA9", ISSN = "0025-5513", MRnumber = "MR 341796", bibdate = "Thu Jan 19 07:19:49 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Mathematica Japonica", } @Article{Nance:1972:BRN, author = "R. E. Nance and C. {Overstreet, Jr.}", title = "A Bibliography on Random Number Generation", journal = j-COMP-REV, volume = "13", number = "??", pages = "495--508", month = "????", year = "1972", CODEN = "CPGRA6", ISSN = "0010-4884, 0149-1202", ISSN-L = "0010-4884", bibdate = "Thu Jan 05 17:41:34 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Computing Reviews", } @TechReport{Nance:1972:IFR, author = "Richard E. Nance and Claude Overstreet", title = "Implementation of {Fortran} random number generators on the {SRU} 1108", type = "Technical report", number = "CP-72022", institution = "Computer Science/Operations Research Center, Institute of Technology, Southern Methodist University", address = "Dallas, TX, USA", pages = "14", year = "1972", bibdate = "Fri Feb 09 17:49:08 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, annote = "Bibliography: p. 14.", } @Article{Neave:1972:CLW, author = "Henry R. Neave", title = "A Comparison of Lag Window Generators", journal = j-J-AM-STAT-ASSOC, volume = "67", number = "337", pages = "152--158", month = mar, year = "1972", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:45 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314217; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2284714", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Neave:1972:RNP, author = "Henry R. Neave", title = "A random number package", journal = "Computer Applications in the Natural and Social Sciences", volume = "14", pages = "55", year = "1972", ISBN = "0-85358-015-4", ISBN-13 = "978-0-85358-015-7", ISSN = "0069-8105", LCCN = "QA298 .N4", bibdate = "Tue Jan 31 11:24:46 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, ajournal = "Comp. Applcns Nat. Soc. Sci.", fjournal = "Computer Applications in the Natural and Social Sciences", subject = "Monte Carlo method; data processing; random number generators", } @Article{Niederreiter:1972:DCP, author = "Harald Niederreiter", title = "Discrepancy and convex programming", journal = j-ANN-MAT-PURA-APPL-4, volume = "93", number = "??", pages = "89--97", month = "????", year = "1972", CODEN = "ANLMAE", ISSN = "0373-3114 (print), 1618-1891 (electronic)", MRnumber = "MR 389828", bibdate = "Thu Jan 19 07:25:09 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Annali di matematica pura ed applicata. Series 4", } @Article{Niederreiter:1972:DPR, author = "Harald Niederreiter", title = "On the Distribution of Pseudo-Random Numbers Generated by the Linear Congruential Method", journal = j-MATH-COMPUT, volume = "26", number = "119", pages = "793--795", month = jul, year = "1972", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database; Parallel/Multi.bib", URL = "http://www.jstor.org/stable/pdfplus/2005109.pdf", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Univ. Illinois, Urbana, IL, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "distribution; linear congruential method; number generation; pseudorandom; random number generation", treatment = "T Theoretical or Mathematical", } @InCollection{Niederreiter:1972:MED, author = "Harald Niederreiter", title = "Methods for estimating discrepancy", crossref = "Zaremba:1972:ANT", pages = "203--236", year = "1972", MRnumber = "MR 354593", bibdate = "Thu Jan 19 07:29:32 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Norman:1972:CPG, author = "J. E. Norman and L. E. Cannon", title = "A computer program for the generation of random variables from any discrete distribution", journal = j-J-STAT-COMPUT-SIMUL, volume = "1", number = "4", pages = "331--348", month = "????", year = "1972", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949657208810026", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", bibdate = "Tue Feb 07 08:44:25 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00949657208810026", abstract = "This paper provides specific directions for the preparation of a discrete pseudo-random number generator computer program using basic machine instructions. The scheme is a table look-up first suggested by Marsaglia. It is applicable to any discrete probability distribution. The general procedure is described for probabilities expressed as fractions in a number system of arbitrary base $ \beta $. A brief example is given using the decimal system. Flow diagrams accompany the directions which will enable an experienced programmer to write the program for any computer system with only modest storage requirements. Results of chi-square tests performed on samples from specific binomial, Poisson, negative binomial, and hypergeometric distributions generated using this procedure are given", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", onlinedate = "20 Mar 2007", } @TechReport{Overstreet:1972:FVP, author = "Claude Overstreet", title = "A {FORTRAN V} package for testing and anaylsis of pseudorandom number generators", type = "Technical report", number = "CP-72009", institution = "Computer Science/Operations Research Center, Institute of Technology, Southern Methodist University", address = "Dallas, TX, USA", pages = "7 + [24]", year = "1972", bibdate = "Fri Feb 09 17:49:23 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, annote = "``A revised and modified version of Technical report CP-700011.'' Bibliography: l. 7.", } @Article{Phillips:1972:PGG, author = "Don T. Phillips and Charles S. Beightler", title = "Procedures for generating gamma variates with non-integer parameter sets", journal = j-J-STAT-COMPUT-SIMUL, volume = "1", number = "3", pages = "197--208", month = "????", year = "1972", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949657208810015", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", bibdate = "Tue Feb 07 08:50:32 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00949657208810015", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", onlinedate = "20 Mar 2007", } @Article{Proll:1972:RAA, author = "L. G. Proll", title = "Remark on ``{ACM Algorithm 370}: {General} random number generator [{G5}]''", journal = j-CACM, volume = "15", number = "6", pages = "467--468", month = jun, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 07:14:04 MST 2001", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1972.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Proll72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Butler:1970:AAG}.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Univ. Southampton, UK", country = "USA", descriptors = "RVG", enum = "7783", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "cumulative distribution function; probability density function; random number generation; random number generator; subroutines; transformation", oldlabel = "Proll72", references = "0", treatment = "G General Review", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Proll72", } @Article{Ramberg:1972:AMG, author = "John S. Ramberg and Bruce W. Schmeiser", title = "Approximate Method for Generating Symmetric Random Variables", journal = j-CACM, volume = "15", number = "11", pages = "987--990", month = nov, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 07:14:55 MST 2001", bibsource = "Compendex database; http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#RambergS72; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A method for generating values of continuous symmetric random variables that is relatively fast, requires essentially no computer memory, and is easy to use is developed. The method, which uses a uniform zero-one random number source, is based on the inverse function of the lambda distribution of Tukey. Since it approximates many of the continuous theoretical distributions and empirical distributions frequently used in simulations, the method should be useful to simulation practitioners.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", classification = "922", corpsource = "Univ. Iowa, Iowa City, IA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", journalabr = "Commun ACM", keywords = "approximate method; inverse function; lambda distribution of Tukey; mathematical models; mathematical statistics; random number generation; random number source; simulation; symmetric random variable generation; uniform zero one", oldlabel = "RambergS72", treatment = "T Theoretical or Mathematical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/RambergS72", } @Article{Rechtschaffen:1972:QSU, author = "R. N. Rechtschaffen", title = "Queuing simulation using a random number generator", journal = j-IBM-SYS-J, volume = "11", number = "3", pages = "255--271", year = "1972", CODEN = "IBMSA7", ISSN = "0018-8670", bibdate = "Tue Mar 19 17:38:46 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "IBM Systems Journal", } @Article{Relles:1972:SAG, author = "Daniel A. Relles", title = "A simple algorithm for generating binomial random variables when {$N$} is large", journal = j-J-AM-STAT-ASSOC, volume = "67", number = "339", pages = "612--613", month = sep, year = "1972", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Fri Jan 6 09:58:59 2012", bibsource = "Distributed/QLD.bib; Distributed/QLD/1972.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2284449", acknowledgement = ack-nhfb, date = "13/05/93", descriptors = "RVG", enum = "7809", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", location = "SEL: Wi", revision = "16/01/94", } @Article{Schincke:1972:EPS, author = "E. Schincke and J. H{\"o}pfner", title = "{Erzeugungen von Pseudozufallszahlenfolgen mit st{\"u}ckweise polygonaler Verteilung}. ({German}) [{Generation} of pseudo random number sequences with piecemeal polynomial distribution]", journal = j-COMPUTING, volume = "9", number = "1", pages = "63--68", month = mar, year = "1972", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", bibdate = "Tue Jan 2 17:40:51 MST 2001", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; INSPEC Axiom database (1968--date)", acknowledgement = ack-nhfb, affiliation = "Martin-Luther Univ., Saale, East Germany", classification = "C7890", description = "random number generation", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", keywords = "algorithm; generation; piecewise continuous probability distributions; pseudorandom numbers; transformation; uniform distribution", language = "German", } @Article{Schrack:1972:RAR, author = "G{\"u}nther F. Schrack", title = "Remark on ``{Algorithm 381}: Random vectors uniform in solid angle''", journal = j-CACM, volume = "15", number = "6", pages = "468--468", month = jun, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 07:19:52 MST 2001", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Schrack72a; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Knop:1970:AAR}.", acknowledgement = ack-nhfb, classcodes = "C7890 (Other special applications of computing)", corpsource = "Univ. British Columbia, Vancouver, BC, Canada", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "points uniform on; random number generation; random vector generator; solid angle; sphere; spherically symmetric probability distribution; subroutines", oldlabel = "Schrack72a", treatment = "A Application", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Schrack72a", } @InCollection{Sobol:1972:DIG, author = "I. M. Sobol'", booktitle = "Operations research and statistical modeling, No. 1 ({Russian})", title = "A deterministic interpretation of goodness-of-fit tests, and a test of pseudorandom numbers", publisher = "Izdat. Leningrad. Univ., Leningrad", pages = "162--169", year = "1972", MRclass = "65C05", MRnumber = "0373221 (51 \#9422)", MRreviewer = "V. Pagurova", bibdate = "Thu Jan 19 08:21:30 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Sobol:1972:PEE, author = "I. M. Sobol'", title = "A probabilistic estimate of the error for nonrandom integration nets", journal = "Voprosy Vy{\c{c}}isl. i Prikl. Mat. (Ta{\v{s}}kent)", volume = "14", number = "??", pages = "5--11", month = "????", year = "1972", CODEN = "????", ISSN = "????", bibdate = "Thu Jan 19 08:22:58 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Sokal:1972:OCN, author = "Nathan O. Sokal", title = "Optimum Choice of Noise Frequency Band and Sampling Rate for Generating Random Binary Digits from Clipped White Noise", journal = j-IEEE-TRANS-COMPUT, volume = "C-21", number = "6", pages = "614--615", month = jun, year = "1972", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/TC.1972.5009023", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Tue Jul 12 18:58:44 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009023", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Sowey:1972:CCB, author = "E. R. Sowey", title = "A Chronological and Classified Bibliography on Random Number Generation and Testing", journal = j-INT-STAT-REV, volume = "40", number = "3", pages = "355--371", month = dec, year = "1972", CODEN = "ISTRDP", ISSN = "0306-7734 (print), 1751-5823 (electronic)", ISSN-L = "0306-7734", bibdate = "Fri Jul 01 07:51:56 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/1402472", acknowledgement = ack-nhfb, fjournal = "International Statistical Review / Revue Internationale de Statistique", journal-URL = "http://www.jstor.org/journals/03067734.html", } @Article{Sullins:1972:CAP, author = "Walter L. Sullins", title = "Certification of ``{Algorithm 266}: {Pseudo}-Random Numbers [{G5}]''", journal = j-CACM, volume = "15", number = "12", pages = "1072--1073", year = "1972", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Aug 02 07:31:49 2004", bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Sullins72; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Pike:1965:APR} and remarks \cite{Hansson:1966:RAG,Pike:1966:RAG}.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "PRNG (pseudo-random number generator)", oldlabel = "Sullins72", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sullins72", } @Article{Vincent:1972:CPA, author = "C. H. Vincent", title = "Corrigendum: {Precautions for accuracy in the generation of truly random binary numbers}", journal = j-J-PHYS-E, volume = "5", number = "6", pages = "546--546", year = "1972", CODEN = "JPSIAE", DOI = "https://doi.org/10.1088/0022-3735/5/6/521", ISSN = "0022-3735", ISSN-L = "0022-3735", bibdate = "Sat Nov 29 15:13:30 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See \cite{Vincent:1971:PAG}.", URL = "http://stacks.iop.org/0022-3735/5/i=6/a=521", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. E: Scientific instruments", journal-URL = "http://iopscience.iop.org/0022-3735/", } @Article{Ahrens:1973:EFM, author = "J. H. Ahrens and Ulrich Dieter", title = "Extensions of {Forsythe}'s method for random sampling from the normal distribution", journal = j-MATH-COMPUT, volume = "27", number = "124", pages = "927--937", month = oct, year = "1973", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "Distributed/QLD.bib; Distributed/QLD/1973.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; JSTOR database", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG", enum = "6927", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Ahrens:1973:NME, author = "J. H. Ahrens and Ulrich Dieter", title = "{Neuere Methoden zur Erzeugung von nicht-gleichverteilten Zufallsvariablen}. ({German}) [{Newer} methods for the generation of nonuniformly distributed random variables]", journal = j-Z-ANGE-MATH-MECH, volume = "53", number = "12", pages = "T221--T223", month = "????", year = "1973", CODEN = "ZAMMAX", DOI = "https://doi.org/10.1002/zamm.197305312115", ISSN = "0044-2267 (print), 1521-4001 (electronic)", ISSN-L = "0044-2267", bibdate = "Mon Jan 16 12:55:37 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/zamm.197305312115/abstract", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001", language = "German", onlinedate = "17 November 2010", } @Article{Burford:1973:BAC, author = "R. L. Burford", title = "A better additive congruential random number generator", journal = "Decision Sciences", volume = "4", number = "??", pages = "190--193", month = "????", year = "1973", CODEN = "????", ISSN = "0011-7315", bibdate = "Mon Jan 16 21:57:00 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @TechReport{Diaconis:1973:LMI, author = "Persi Diaconis", title = "Limits of measures of the integers with applications to random number generators and the distribution of leading digits", type = "Memorandum", number = "NS-211", institution = "Department of Statistics, Harvard University", address = "Cambridge, MA, USA", day = "22", month = mar, year = "1973", bibdate = "Sat Nov 12 16:23:20 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, } @Article{Dieter:1973:CMG, author = "Ulrich Dieter and J. H. Ahrens", title = "A Combinatorial Method for the Generation of Normally Distributed Random Numbers", journal = j-COMPUTING, volume = "11", number = "2", pages = "137--146", month = jun, year = "1973", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", bibdate = "Tue Jan 2 17:40:51 MST 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; INSPEC Axiom database (1968--date)", acknowledgement = ack-ec # " and " # ack-nhfb, affiliation = "Tech. Hochschule Graz, Austria", classification = "C7890", description = "random number generation", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", keywords = "combinatorial method; generation; normally distributed; random numbers", } @Book{Durbin:1973:DTT, author = "James Durbin", title = "Distribution Theory for Tests Based on the Sample Distribution Function", volume = "9", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "vi + 64", year = "1973", LCCN = "QA276.7 .D87", bibdate = "Sat Mar 03 15:01:34 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", series = "SIAM CBMS-NSF Regional Conference Series in applied mathematics", acknowledgement = ack-nhfb, } @Book{Fishman:1973:CMD, author = "George S. Fishman", title = "Concepts and Methods in Discrete Event Digital Simulation", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiv + 385", year = "1973", ISBN = "0-471-26155-6", ISBN-13 = "978-0-471-26155-1", LCCN = "T57.62 .F57", bibdate = "Thu Jan 5 14:27:20 MST 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, subject = "Digital computer simulation; System analysis", } @Article{Good:1973:BRB, author = "I. J. Good", title = "Book Review: {{\booktitle{The Generation of Random Variates}} by T. G. Newman; P. L. Odell}", journal = j-INT-STAT-REV, volume = "41", number = "1", pages = "139--140", month = apr, year = "1973", CODEN = "ISTRDP", DOI = "https://doi.org/10.2307/1402798", ISSN = "0306-7734 (print), 1751-5823 (electronic)", ISSN-L = "0306-7734", bibdate = "Wed Jun 18 06:09:08 MDT 2014", bibsource = "http://www.jstor.org/stable/i261080; https://www.math.utah.edu/pub/tex/bib/intstatrev.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/1402798", acknowledgement = ack-nhfb, fjournal = "International Statistical Review = Revue Internationale de Statistique", journal-URL = "http://www.jstor.org/journals/03067734.html", } @PhdThesis{Grube:1973:MREa, author = "A. Grube", title = "{Mehrfach rekursiv erzeugte Zahienfolgen} ({German}) [Multiple sequences of numbers generated recursively]", type = "Dissertation", school = "Fakult{\"a}t f{\"u}r Mathematik, Universit{\"a}t Karlsruhe", address = "Karlsruhe, West Germany", year = "1973", bibdate = "Tue Jan 10 16:09:20 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Grube:1973:MREb, author = "A. Grube", title = "{Mehrfach rekursiv-erzeugte Pseudo-Zufallszahlen}. ({German}) [{Multiply} recursive generation of pseudorandom numbers]", journal = j-Z-ANGE-MATH-MECH, volume = "53", number = "12", pages = "T223--T225", month = "????", year = "1973", CODEN = "ZAMMAX", DOI = "https://doi.org/10.1002/zamm.197305312116", ISSN = "0044-2267 (print), 1521-4001 (electronic)", ISSN-L = "0044-2267", bibdate = "Mon Jan 16 21:57:34 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001", language = "German", } @Article{Gupta:1973:OSE, author = "Shanti S. Gupta and Klaus Nagel and S. Panchapakesan", title = "On the Order Statistics from Equally Correlated Normal Random Variables", journal = j-BIOMETRIKA, volume = "60", number = "2", pages = "403--413", month = aug, year = "1973", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2334554", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", MRclass = "62E15", MRnumber = "0388608 (52 \#9444)", MRreviewer = "R. E. Barlow", bibdate = "Sat Jun 21 14:33:52 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315474; https://www.math.utah.edu/pub/tex/bib/biometrika1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2334554", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", } @Article{Hader:1973:IMR, author = "R. J. Hader", title = "An Improper Method of Randomization in Experimental Design", journal = j-AMER-STAT, volume = "27", number = "2", pages = "82--84", month = apr, year = "1973", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 10:52:20 MST 2012", bibsource = "http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326378; https://www.math.utah.edu/pub/tex/bib/amstat1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.jstor.org/stable/2683964", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Book{Hamming:1973:NMS, author = "R. W. Hamming", title = "Numerical Methods for Scientists and Engineers", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, edition = "Second", pages = "ix + 721", year = "1973", ISBN = "0-07-025887-2", ISBN-13 = "978-0-07-025887-7", LCCN = "QA297 .H28 1973", bibdate = "Tue Jan 17 11:46:24 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, keywords = "random numbers", } @Article{Holland:1973:GAO, author = "John H. Holland", key = "genetic-algorithms", title = "Genetic Algorithms and the Optimal Allocation of Trials", journal = j-SIAM-J-COMPUT, volume = "2", number = "2", pages = "88--105", month = apr, year = "1973", CODEN = "SMJCAT", ISSN = "0097-5397 (print), 1095-7111 (electronic)", ISSN-L = "0097-5397", bibdate = "Mon Nov 29 10:57:42 MST 2010", bibsource = "Ai/alife.bib; http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/2; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib; Misc/misc.1.bib", note = "See erratum \cite{Holland:1974:EGA}.", abstract = "This study gives a formal setting to the difficult optimisation problems characterised by the conjunction of (1) substantial complexity and initial uncertainty, (2) the necessity of acquiring new information rapidly to reduce the uncertainty and (3) a requirement that the new information be exploited as acquired so that average performance increases at a rate consistent with th rate of acquisition of information. The setting has as its basis a set A of structures to be searched or tried and a performance function u:A->real numbers. Within this setting it is determined how to allocate trials to a set of random variables so as to maximise expected performances. This result is then transformed into a criterion against which to measure the performance of a robust and easily implemented set of algorithms called reproductive plans. It is shown that reproductive plans can in fact surpass the criterion because of a phenomenon called intrinsic parallelism --- a single trial (individual a E A) simultaneously tests and exploits many random variables.", acknowledgement = ack-nhfb, annote = "A mathematical analysis of genetic algorithms and their ``implicit parallelism''.", fjournal = "SIAM Journal on Computing", journal-URL = "http://epubs.siam.org/sicomp", } @Article{Knop:1973:AAR, author = "Robert E. Knop", title = "{ACM Algorithm 441}: Random Deviates from the Dipole Distribution [{G5}]", journal = j-CACM, volume = "16", number = "1", pages = "51--51", month = jan, year = "1973", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 06:55:18 MST 2001", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Knop73; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/fortran1.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics computing)", corpsource = "Florida State Univ., Tallahassee, FL, USA", country = "USA", descriptors = "RVG", enum = "7514", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", keywords = "dipole distribution; FORTRAN; probability density; random deviates; random number; statistics; subroutines", oldlabel = "Knop73", references = "0", treatment = "P Practical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Knop73", } @Article{Kozlov:1973:EEM, author = "G. A. Kozlov", title = "Estimation of the Error of the Method of Statistical Tests ({Monte-Carlo}) Due to Imperfections in the Distribution of Random Numbers", journal = j-THEORY-PROBAB-APPL, volume = "17", number = "3", pages = "493--509", month = "????", year = "1973", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/1117057", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Tue Apr 1 10:36:41 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/17/3; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib", acknowledgement = ack-nhfb, ajournal = "Theory Probab. Appl.", fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", onlinedate = "June 1973", } @TechReport{Learmonth:1973:NPS, author = "G. P. Learmonth and P. A. W. Lewis", title = "{Naval Postgraduate School} Random Number Generator Package {LLRANDOM}", type = "Report", number = "NP555LW73061A", institution = "Naval Postgraduate School", address = "Monterey, CA, USA", year = "1973", bibdate = "Thu Jan 05 14:33:09 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "The shuffling algorithm proposed in this report does {\em not\/} lengthen the period, and only marginally reduces the lattice structure of linear congruential generators, despite the apparently tiny difference with the \cite{Bays:1976:IPR} algorithm: see \cite{Bays:1990:CIR} for a comparison, both mathematical, and graphical.", acknowledgement = ack-nhfb, } @Article{Levin:1973:NRS, author = "L. A. Levin", title = "On the notion of a random sequence", journal = j-SOVIET-MATH-DOKL, volume = "14", number = "??", pages = "1413--1416", month = "????", year = "1973", CODEN = "????", ISSN = "0197-6788", bibdate = "Thu Dec 29 15:04:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, fjournal = "Soviet Mathematics. Doklady", } @Article{Lewis:1973:GFS, author = "T. G. Lewis and W. G. Payne", title = "Generalized Feedback Shift Register Pseudorandom Number Algorithm", journal = j-J-ACM, volume = "20", number = "3", pages = "456--468", month = jul, year = "1973", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321765.321777", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Thu Dec 22 07:42:23 2011", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", note = "See important errata, and algorithm and code improvements, in \cite{Fushimi:1990:RNG}.", acknowledgement = ack-nhfb, annote = "Feedback configurations for SR's of length > 45", descriptors = "Shift register sequences", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @TechReport{Malcolm:1973:UUR, author = "Michael A. Malcolm and Cleve B. Moler", title = "{URAND}: a universal random number generator", type = "Technical Report", number = "STAN-CS-73-334", institution = "Computer Science Department, Stanford University", address = "Stanford, CA, USA", pages = "5", year = "1973", bibdate = "Sat Apr 07 09:25:30 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", abstract = "A subroutine for generating uniformly-distributed floating-point numbers in the interval $ [0, 1) $ is presented in ANSI Standard Fortran. The subroutine, URAND, is designed to be relatively machine independent. URAND has undergone minimal testing on various machines and is thought to work properly on any machine having binary integer number representation, integer multiplication modulo $m$ and integer addition either modulo $m$ or yielding at least $ \log_2 (m) $ significant bits, where $m$ is some integral power of $2$. Upon the first call of URAND, the value of $m$ is automatically determined and appropriate constants for a linear congruential generator are computed following the suggestions of D. E. Knuth, volume 2. URAND is guaranteed to have a full-length cycle. Readers are invited to apply their favorite statistical tests to URAND, using any binary machine, and report the results to the authors.", acknowledgement = ack-nhfb, } @Article{Maritsas:1973:AFT, author = "D. G. Maritsas", title = "The Autocorrelation Function of the Two Feedback Shift-Register Pseudorandom Source", journal = j-IEEE-TRANS-COMPUT, volume = "C-22", number = "10", pages = "962--964", month = oct, year = "1973", CODEN = "ITCOB4", DOI = "https://doi.org/10.1109/T-C.1973.223626", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Tue Jul 12 16:45:35 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672219", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Maritsas:1973:HSA, author = "Dimitris G. Maritsas", title = "A High Speed and Accuracy Digital {Gaussian} Generator of Pseudorandom Numbers", journal = j-IEEE-TRANS-COMPUT, volume = "C-22", number = "7", pages = "629--634", month = jul, year = "1973", CODEN