stats::kurtosis -- kurtosis
(excess)
Introductionstats::kurtosis(data) returns the kurtosis
(the coefficient of excess) of the data.
Call(s)stats::kurtosis(x1, x2, ..)
stats::kurtosis([x1, x2, ..])
stats::kurtosis(s <, c>)
Parametersx1, x2, .. |
- | the statistical data: arithmetical expressions. |
s |
- | a sample of domain type stats::sample. |
c |
- | an integer representing a column index of the sample
s. This column provides the data x1,
x2 etc. |
Returnsan arithmetical expression. FAIL is returned, if the
kurtosis does not exist.
Related
Functions
Details
(1/n*((x[1] - X)^4 + .. +(x[n] - X)^4)) /
(1/n*((x[1] - X)^2 + .. +(x[n] - X)^2))^2 - 3 ,
where X is the mean value of the x[i]. The
kurtosis measures whether a distribution is ``flat'' or ``peaked''. For
normally distributed data the kurtosis is zero. If the distribution
function of the data has a flatter top than the normal distribution,
then the kurtosis is negative. The kurtosis is positive, if the
distribution function has a high peak, compared to the normal
distribution.c is optional, if the data are given
by a stats::sample
object containing only one non-string column. Cf. example 3.
Example
1We calculate the kurtosis of some values:
>> stats::kurtosis(0, 7, 7, 6, 6, 6, 5, 5, 4, 1)
-74146/271441
Alternatively, the data may be passed as a list:
>> stats::kurtosis([2, 2, 4, 6, 8, 10, 10])
-85/54
Example
2We create a sample:
>> stats::sample([[a, 5, 8], [b, 3, 7], [c, d, 0]])
a 5 8
b 3 7
c d 0
The kurtosis of the second column is:
>> stats::kurtosis(%, 2)
/ d \4 / d \4 / 2 d \4
3 | 1/3 - - | + 3 | 7/3 - - | + 3 | --- - 8/3 |
\ 3 / \ 3 / \ 3 /
-------------------------------------------------- - 3
/ / d \2 / d \2 / 2 d \2 \2
| | 1/3 - - | + | 7/3 - - | + | --- - 8/3 | |
\ \ 3 / \ 3 / \ 3 / /
Example
3We create a sample consisting of one string column and one non-string column:
>> stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])
"1996" 1242
"1997" 1353
"1998" 1142
We compute the kurtosis of the second column. In this case this column does not have to be specified, since it is the only non-string column:
>> stats::kurtosis(%)
-3/2