skewness: Skewness

Description

compute skewness of a univariate distribution.

Usage

skewness(x, na.rm = FALSE,
    method = c("moment", "fisher", "sample"), ...)

Arguments

na.rm

a logical. Should missing values be removed?

method

a character string which specifies the method of computation. These are either "moment" or "fisher" The "moment" method is based on the definitions of skewnessfor distributions; these forms should be used whe

a numeric vector or object.

...

arguments to be passed.

Details

This function was ported from the RMetrics package fUtilities to eliminate a dependency on fUtiltiies being loaded every time. The function is identical except for the addition of

checkData and column
  support.

$$Skewness(moment) = \frac{1}{n}*\sum^{n}_{i=1}(\frac{r_i - \overline{r}}{\sigma_P})^3$$ $$Skewness(sample) = \frac{n}{(n-1)*(n-2)}*\sum^{n}_{i=1}(\frac{r_i - \overline{r}}{\sigma_{S_P}})^3$$ $$Skewness(fisher) = \frac{\frac{\sqrt{n*(n-1)}}{n-2}*\sum^{n}_{i=1}\frac{x^3}{n}}{\sum^{n}_{i=1}(\frac{x^2}{n})^{3/2}}$$

where $n$ is the number of return, $\overline{r}$ is the mean of the return distribution, $\sigma_P$ is its standard deviation and $\sigma_{S_P}$ is its sample standard deviation

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.83-84

Examples

Run this code

## mean -
## var -
   # Mean, Variance:
   r = rnorm(100)
   mean(r)
   var(r)

## skewness -
   skewness(r)
data(managers)
skewness(managers)