R: Skewness

skewness {modeest}

R Documentation

Skewness

Description

The skewness.default function from package fBasics is completed in order to implement Bickel's measure of skewness, based on the mode of the distribution considered.

Usage

skewness(x, 
         ...)

  ## Default S3 method:
skewness(x, 
         na.rm = FALSE, 
         method = c("moment", "fisher", "bickel"), 
         M = shorth(x), 
         ...)

Arguments

`x`	numeric. Vector of observations.
`na.rm`	logical. Should missing values be removed?
`method`	character. Specifies the method of computation. These are either `"moment"`, `"fisher"` or `"bickel"`. The `"moment"` method is based on the definition of skewness for distributions; this form should be used when resampling (bootstrap or jackknife). The `"fisher"` method corresponds to the usual "unbiased" definition of sample variance, although in the case of skewness exact unbiasedness is not possible.
`M`	numeric. (An estimate of) the mode of the observations `x`. Default value is `shorth(x)`.
`...`	arguments to be passed.

Value

skewness returns a numeric value. An attribute which reports the method used is added.

Author(s)

Diethelm Wuertz and other authors for the original skewness function from package fBasics;
P. Poncet for the slight modification introduced.

References

Bickel D.R. (2002). Robust estimators of the mode and skewness of continuous data. Computational Statistics and Data Analysis, 39:153-163.
Bickel D.R. et Fruehwirth R. (2006). On a Fast, Robust Estimator of the Mode: Comparisons to Other Robust Estimators with Applications. Computational Statistics and Data Analysis, 50(12):3500-3530.

Examples

## Skewness = 0
x <- rnorm(1000)
skewness(x, method = "bickel", M = shorth(x))

## Skewness > 0 (left skewed case)
x <- rbeta(1000, 2, 5)
skewness(x, method = "bickel", M = betaMode(2, 5))

## Skewness < 0 (right skewed case)
x <- rbeta(1000, 7, 2)
skewness(x, method = "bickel", M = hsm(x, bw = 1/3))

[Package modeest version 2.1 Index]