kurtosis {e1071} | R Documentation |
Computes the kurtosis.
kurtosis(x, na.rm = FALSE, type = 3)
x |
a numeric vector containing the values whose kurtosis is to be computed. |
na.rm |
a logical value indicating whether |
type |
an integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below. |
If x
contains missings and these are not removed, the skewness
is NA
.
Otherwise, write x_i for the non-missing elements of x
,
n for their number, mu for their mean, s for
their standard deviation, and
m_r = ∑_i (x_i - mu)^r / n
for the sample moments of order r.
Joanes and Gill (1998) discuss three methods for estimating kurtosis:
. This is the typical definition used in many older textbooks.
. Used in SAS and SPSS.
. Used in MINITAB and BMDP.
Only G_2 (corresponding to type = 2
) is unbiased under
normality.
The estimated kurtosis of x
.
D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183–189.
x <- rnorm(100) kurtosis(x)