SUBROUTINE stat(x,n,av,var,xmin,xmax) C********************************************************************** C C SUBROUTINE STAT( X, N, AV, VAR) C C compute STATistics C C C Function C C C Computes AVerage and VARiance of array X(N). C C********************************************************************** C .. Scalar Arguments .. REAL av,var,xmax,xmin INTEGER n C .. C .. Array Arguments .. REAL x(n) C .. C .. Local Scalars .. REAL sum INTEGER i C .. C .. Intrinsic Functions .. INTRINSIC real C .. C .. Executable Statements .. xmin = x(1) xmax = x(1) sum = 0.0 DO 10,i = 1,n sum = sum + x(i) IF (x(i).LT.xmin) xmin = x(i) IF (x(i).GT.xmax) xmax = x(i) 10 CONTINUE av = sum/real(n) sum = 0.0 DO 20,i = 1,n sum = sum + (x(i)-av)**2 20 CONTINUE var = sum/real(n-1) RETURN END PROGRAM tstall IMPLICIT LOGICAL (q) C Interactive test for PHRTSD C .. Parameters .. INTEGER mxwh,mxncat PARAMETER (mxwh=15,mxncat=100) C .. C .. Local Scalars .. REAL av,avtr,var,vartr,xmin,xmax,pevt,psum,rtry INTEGER i,is1,is2,itmp,iwhich,j,mxint,nperm,nrep,ntot,ntry,ncat CHARACTER type*4,phrase*100 C .. C .. Local Arrays .. REAL array(1000),param(3),prob(mxncat) INTEGER iarray(1000),perm(500) C .. C .. External Functions .. REAL genbet,genchi,genf,gennch,gennf,genunf,genexp,gengam,gennor INTEGER ignuin,ignnbn EXTERNAL genbet,genchi,genf,gennch,gennf,genunf,ignuin C .. C .. External Subroutines .. EXTERNAL genprm,phrtsd,setall,stat,trstat,genmul C .. C .. Executable Statements .. WRITE (*,9000) 9000 FORMAT (' Tests most generators of specific distributions.'/ + ' Generates 1000 deviates: reports mean and variance.'/ + ' Also reports theoretical mean and variance.'/ + ' If theoretical mean or var doesn''t exist prints -1.'/ + ' For permutations, generates one permutation of 1..n'/ + ' and prints it.'/ + ' For uniform integers asks for upper bound, number of'/ + ' replicates per integer in 1..upper bound.'/ + ' Prints table of num times each integer generated.'/ + ' For multinomial asks for number of events to be'/ + ' classified, number of categories in which they'/ + ' are to be classified, and the probabilities that'/ + ' an event will be classified in the categories,'/ + ' for all but the last category. Prints table of'/ + ' number of events by category, true probability'/ + ' associated with each category, and observed'/ + ' proportion of events in each category.') C C Menu for choosing tests C 10 WRITE (*,9010) 9010 FORMAT (' Enter number corresponding to choice:'/ + ' (0) Exit this program'/ + ' (1) Generate Chi-Square deviates'/ + ' (2) Generate noncentral Chi-Square deviates'/ + ' (3) Generate F deviates'/ + ' (4) Generate noncentral F deviates'/ + ' (5) Generate random permutation'/ + ' (6) Generate uniform integers'/ + ' (7) Generate uniform reals'/ + ' (8) Generate beta deviates'/ + ' (9) Generate binomial outcomes'/ + ' (10) Generate Poisson outcomes'/ + ' (11) Generate exponential deviates'/ + ' (12) Generate gamma deviates'/ + ' (13) Generate multinomial outcomes'/ + ' (14) Generate normal deviates'/ + ' (15) Generate negative binomial outcomes'/) READ (*,*) iwhich IF (.NOT. (iwhich.LT.0.OR.iwhich.GT.mxwh)) GO TO 20 WRITE (*,*) ' Choices are 1..',mxwh,' - try again.' GO TO 10 20 IF (iwhich.EQ.0) STOP ' Normal termination rn tests' WRITE (*,*) ' Enter phrase to initialize rn generator' READ (*,'(a)') phrase CALL phrtsd(phrase,is1,is2) CALL setall(is1,is2) IF ((1).NE. (iwhich)) GO TO 40 C C Chi-square deviates C type = 'chis' WRITE (*,*) ' Enter (real) df for the chi-square generation' READ (*,*) param(1) DO 30,i = 1,1000 array(i) = genchi(param(1)) 30 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax 9020 FORMAT (' Mean Generated: ',T30,G15.7,5X,'True:',T60, + G15.7/' Variance Generated:',T30,G15.7,5X,'True:',T60, + G15.7/' Minimum: ',T30,G15.7,5X,'Maximum:',T60,G15.7) GO TO 420 40 IF ((2).NE. (iwhich)) GO TO 60 C C Noncentral Chi-square deviates C type = 'ncch' WRITE (*,*) ' Enter (real) df' WRITE (*,*) ' (real) noncentrality parameter' READ (*,*) param(1),param(2) DO 50,i = 1,1000 array(i) = gennch(param(1),param(2)) 50 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 60 IF ((3).NE. (iwhich)) GO TO 80 C C F deviates C type = 'f' WRITE (*,*) ' Enter (real) df of the numerator' WRITE (*,*) ' (real) df of the denominator' READ (*,*) param(1),param(2) DO 70,i = 1,1000 array(i) = genf(param(1),param(2)) 70 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 80 IF ((4).NE. (iwhich)) GO TO 100 C C Noncentral F deviates C type = 'ncf' WRITE (*,*) ' Enter (real) df of the numerator' WRITE (*,*) ' (real) df of the denominator' WRITE (*,*) ' (real) noncentrality parameter' READ (*,*) param(1),param(2),param(3) DO 90,i = 1,1000 array(i) = gennf(param(1),param(2),param(3)) 90 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 100 IF ((5).NE. (iwhich)) GO TO 140 C C Random permutation C 110 WRITE (*,*) ' Enter size of permutation' READ (*,*) nperm IF (.NOT. (nperm.LT.1.OR.nperm.GT.500)) GO TO 120 WRITE (*,*) ' Permutation size must be between 1 and 500 ', + '- try again!' GO TO 110 120 WRITE (*,*) ' Random Permutation Generated - Size',nperm DO 130,i = 1,500 perm(i) = i 130 CONTINUE CALL genprm(perm,nperm) WRITE (*,*) ' Perm Generated' WRITE (*,'(20I4)') (perm(i),i=1,nperm) GO TO 420 140 IF ((6).NE. (iwhich)) GO TO 170 C C Uniform integer C WRITE (*,*) ' Enter maximum uniform integer' READ (*,*) mxint WRITE (*,*) ' Enter number of replications per integer' READ (*,*) nrep DO 150,i = 1,1000 iarray(i) = 0 150 CONTINUE ntot = mxint*nrep DO 160,i = 1,ntot itmp = ignuin(1,mxint) iarray(itmp) = iarray(itmp) + 1 160 CONTINUE WRITE (*,*) ' Counts of Integers Generated' WRITE (*,'(20I4)') (iarray(j),j=1,mxint) GO TO 420 170 IF ((7).NE. (iwhich)) GO TO 190 C C Uniform real C type = 'unif' WRITE (*,*) ' Enter Low then High bound for uniforms' READ (*,*) param(1),param(2) DO 180,i = 1,1000 array(i) = genunf(param(1),param(2)) 180 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 190 IF ((8).NE. (iwhich)) GO TO 210 C C Beta deviate C type = 'beta' WRITE (*,*) ' Enter A, B for Beta deviate' READ (*,*) param(1),param(2) DO 200,i = 1,1000 array(i) = genbet(param(1),param(2)) 200 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 210 IF ((9).NE. (iwhich)) GO TO 240 C C Binomial outcomes C type = 'bin' WRITE (*,*) ' Enter number of trials, Prob event for ', + 'binomial outcomes' READ (*,*) ntry,pevt DO 220,i = 1,1000 iarray(i) = ignbin(ntry,pevt) 220 CONTINUE DO 230,i = 1,1000 array(i) = iarray(i) 230 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) param(1) = ntry param(2) = pevt CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 240 IF ((10).NE. (iwhich)) GO TO 270 C C Poisson outcomes C type = 'pois' WRITE (*,*) ' Enter mean for Poisson generation' READ (*,*) param(1) DO 250,i = 1,1000 iarray(i) = ignpoi(param(1)) 250 CONTINUE DO 260,i = 1,1000 array(i) = iarray(i) 260 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 270 IF ((11).NE. (iwhich)) GO TO 290 C C Exponential deviates C type = 'expo' WRITE (*,*) ' Enter (real) AV for Exponential' READ (*,*) param(1) DO 280,i = 1,1000 array(i) = genexp(param(1)) 280 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 290 IF ((12).NE. (iwhich)) GO TO 310 C C Gamma deviates C type = 'gamm' WRITE (*,*) ' Enter (real) A, (real) R for Gamma deviate' READ (*,*) param(1),param(2) DO 300,i = 1,1000 array(i) = gengam(param(1),param(2)) 300 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 310 IF ((13).NE. (iwhich)) GO TO 360 C C Multinomial outcomes C WRITE (*,*) ' Enter (int) number of observations: ' READ (*,*) ntry 320 WRITE (*,*) ' Enter (int) num. of categories: <= ',mxncat READ (*,*) ncat IF (ncat.GT.mxncat) THEN WRITE (*,*) ' number of categories must be <= ',mxncat WRITE (*,*) ' Try again ... ' GO TO 320 END IF WRITE (*,*) ' Enter (real) prob. vector of length ',ncat-1 READ (*,*) (prob(i),i=1,ncat-1) CALL genmul(ntry,prob,ncat,iarray) ntot = 0 IF (ntry.GT.0) THEN rtry = real(ntry) DO 330, i = 1,ncat ntot = ntot + iarray(i) array(i) = iarray(i)/rtry 330 CONTINUE ELSE DO 340, i = 1,ncat ntot = ntot + iarray(i) array(i) = 0.0 340 CONTINUE ENDIF psum = 0.0 DO 350, i = 1,ncat-1 psum = psum + prob(i) 350 CONTINUE prob(ncat) = 1.0 - psum WRITE (*,*) ' Total number of observations: ',ntot WRITE (*,*) ' Total observations by category: ' WRITE (*,'(10I8)') (iarray(i),i=1,ncat) WRITE (*,*) ' True probabilities by category: ' WRITE (*,'(8F10.7)') (prob(i),i=1,ncat) WRITE (*,*) ' Observed proportions by category: ' WRITE (*,'(8F10.7)') (array(i),i=1,ncat) GO TO 420 360 IF ((14).NE. (iwhich)) GO TO 380 C C Normal deviates C type = 'norm' WRITE (*,*) ' Enter (real) AV, (real) SD for Normal' READ (*,*) param(1),param(2) DO 370,i = 1,1000 array(i) = gennor(param(1),param(2)) 370 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 380 IF ((15).NE. (iwhich)) GO TO 410 C C Negative Binomial outcomes C type = 'nbin' WRITE (*,*) ' Enter required (int) Number of events then ' WRITE (*,*) ' (real) Prob of an event for negative binomial' READ (*,*) ntry,pevt DO 390,i = 1,1000 iarray(i) = ignnbn(ntry,pevt) 390 CONTINUE DO 400,i = 1,1000 array(i) = iarray(i) 400 CONTINUE CALL stat(array,1000,av,var,xmin,xmax) param(1) = ntry param(2) = pevt CALL trstat(type,param,avtr,vartr) WRITE (*,9020) av,avtr,var,vartr,xmin,xmax GO TO 420 410 CONTINUE 420 GO TO 10 END SUBROUTINE trstat(type,parin,av,var) IMPLICIT INTEGER (i-n),REAL (a-h,o-p,r-z),LOGICAL (q) C********************************************************************** C C SUBROUTINE TRSTAT( TYPE, PARIN, AV, VAR ) C TRue STATistics C C Returns mean and variance for a number of statistical distribution C as a function of their parameters. C C C Arguments C C C TYPE --> Character string indicating type of distribution C 'chis' chisquare C 'ncch' noncentral chisquare C 'f' F (variance ratio) C 'ncf' noncentral f C 'unif' uniform C 'beta' beta distribution C 'bin' binomial C 'pois' poisson C 'expo' exponential C 'gamm' gamma C 'norm' normal C 'nbin' negative binomial C CHARACTER*(4) TYPE C C PARIN --> Array containing parameters of distribution C chisquare C PARIN(1) is df C noncentral chisquare C PARIN(1) is df C PARIN(2) is noncentrality parameter C F (variance ratio) C PARIN(1) is df numerator C PARIN(2) is df denominator C noncentral F C PARIN(1) is df numerator C PARIN(2) is df denominator C PARIN(3) is noncentrality parameter C uniform C PARIN(1) is LOW bound C PARIN(2) is HIGH bound C beta C PARIN(1) is A C PARIN(2) is B C binomial C PARIN(1) is Number of trials C PARIN(2) is Prob Event at Each Trial C poisson C PARIN(1) is Mean C exponential C PARIN(1) is Mean C gamma C PARIN(1) is A C PARIN(2) is R C normal C PARIN(1) is Mean C PARIN(2) is Standard Deviation C negative binomial C PARIN(1) is required Number of events C PARIN(2) is Probability of event C REAL PARIN(*) C C AV <-- Mean of specified distribution with specified parameters C REAL AV C C VAR <-- Variance of specified distribution with specified paramete C REAL VAR C C C Note C C C AV and Var will be returned -1 if mean or variance is infinite C C********************************************************************** C .. Scalar Arguments .. REAL av,var CHARACTER type* (4) C .. C .. Array Arguments .. REAL parin(*) C .. C .. Local Scalars .. REAL a,b,range C .. C .. Executable Statements .. IF (('chis').NE. (type)) GO TO 10 av = parin(1) var = 2.0*parin(1) GO TO 210 10 IF (('ncch').NE. (type)) GO TO 20 a = parin(1) + parin(2) b = parin(2)/a av = a var = 2.0*a* (1.0+b) GO TO 210 20 IF (('f').NE. (type)) GO TO 70 IF (.NOT. (parin(2).LE.2.0001)) GO TO 30 av = -1.0 GO TO 40 30 av = parin(2)/ (parin(2)-2.0) 40 IF (.NOT. (parin(2).LE.4.0001)) GO TO 50 var = -1.0 GO TO 60 50 var = (2.0*parin(2)**2* (parin(1)+parin(2)-2.0))/ + (parin(1)* (parin(2)-2.0)**2* (parin(2)-4.0)) 60 GO TO 210 70 IF (('ncf').NE. (type)) GO TO 120 IF (.NOT. (parin(2).LE.2.0001)) GO TO 80 av = -1.0 GO TO 90 80 av = (parin(2)* (parin(1)+parin(3)))/ ((parin(2)-2.0)*parin(1)) 90 IF (.NOT. (parin(2).LE.4.0001)) GO TO 100 var = -1.0 GO TO 110 100 a = (parin(1)+parin(3))**2 + (parin(1)+2.0*parin(3))* + (parin(2)-2.0) b = (parin(2)-2.0)**2* (parin(2)-4.0) var = 2.0* (parin(2)/parin(1))**2* (a/b) 110 GO TO 210 120 IF (('unif').NE. (type)) GO TO 130 range = parin(2) - parin(1) av = parin(1) + range/2.0 var = range**2/12.0 GO TO 210 130 IF (('beta').NE. (type)) GO TO 140 av = parin(1)/ (parin(1)+parin(2)) var = (av*parin(2))/ ((parin(1)+parin(2))* + (parin(1)+parin(2)+1.0)) GO TO 210 140 IF (('bin').NE. (type)) GO TO 150 av = parin(1)*parin(2) var = av* (1.0-parin(2)) GO TO 210 150 IF (('pois').NE. (type)) GO TO 160 av = parin(1) var = parin(1) GO TO 210 160 IF (('expo').NE. (type)) GO TO 170 av = parin(1) var = parin(1)**2 GO TO 210 170 IF (('gamm').NE. (type)) GO TO 180 av = parin(2) / parin(1) var = av / parin(1) GO TO 210 180 IF (('norm').NE. (type)) GO TO 190 av = parin(1) var = parin(2)**2 GO TO 210 190 IF (('nbin').NE. (type)) GO TO 200 av = parin(1) * (1.0 - parin(2)) / parin(2) var = av / parin(2) GO TO 210 200 WRITE (*,*) 'Unimplemented type ',type STOP 'Unimplemented type in TRSTAT' 210 RETURN END