# skewness: Skewness In modeest: Mode Estimation

## Description

This function encodes different methods to calculate the skewness from a vector of observations.

## Usage

 `1` ```skewness(x, na.rm = FALSE, method = c("moment", "fisher", "bickel"), M, ...) ```

## 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)`. `...` Additional arguments.

## Value

`skewness` returns a numeric value. An attribute reports the method used.

## Author(s)

Diethelm Wuertz and contributors for the original `skewness` function from package fBasics.

## 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.

`mlv` for general mode estimation; `shorth` for the shorth estimate of the mode
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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)) ```