DistributionUtils (version 0.6-1)

Sample Moments: Sample Skewness and Kurtosis

Description

Computes the sample skewness and sample kurtosis.

Usage

skewness(x, na.rm = FALSE)
kurtosis(x, na.rm = FALSE)

Value

The skewness or kurtosis of x.

Arguments

x

A numeric vector containing the values whose skewness or kurtosis is to be computed.

na.rm

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

Author

Evgenia Dimitriadou, Kurt Hornik, Friedrich Leisch, David Meyer, and Andreas Weingessel

Details

If $N=\mathrm{length}(x)$, then the skewness of $x$ is defined as $$N^{-1}\mathrm{sd}(x{)}^{-3}\sum _i(x_i-\mathrm{mean}(x){)}^3.$$

If $N=\mathrm{length}(x)$, then the kurtosis of $x$ is defined as $$N^{-1}\mathrm{sd}(x{)}^{-4}\sum _i(x_i-\mathrm{mean}(x){)}^4-3.$$

Examples

x <- rnorm(100)
skewness(x)
kurtosis(x)