# kurtosis

0th

Percentile

##### Kurtosis

Computes the kurtosis.

Keywords
univar
##### Usage
kurtosis(x, na.rm = FALSE, type = 3)
##### Arguments
x

a numeric vector containing the values whose kurtosis is to be computed.

na.rm

a logical value indicating whether NA values should be stripped before the computation proceeds.

type

an integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below.

##### Details

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 $m_r = \sum_i (x_i - \mu)^r / n$ for the sample moments of order $r$.

Joanes and Gill (1998) discuss three methods for estimating kurtosis:

Type 1:

$g_2 = m_4 / m_2^2 - 3$. This is the typical definition used in many older textbooks.

Type 2:

$G_2 = ((n+1) g_2 + 6) * (n-1) / ((n-2)(n-3))$. Used in SAS and SPSS.

Type 3:

$b_2 = m_4 / s^4 - 3 = (g_2 + 3) (1 - 1/n)^2 - 3$. Used in MINITAB and BMDP.

Only $G_2$ (corresponding to type = 2) is unbiased under normality.

##### Value

The estimated kurtosis of x.

##### References

D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183--189.

• kurtosis
##### Examples
# NOT RUN {
x <- rnorm(100)
kurtosis(x)
# }

Documentation reproduced from package e1071, version 1.7-3, License: GPL-2 | GPL-3

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