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)