compute skewness of a univariate distribution.

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

x

a numeric vector or object.

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 when resampling (bootstrap or jackknife). The `"fisher"`

method correspond to the usual "unbiased" definition of sample variance,
although in the case of skewness exact unbiasedness is not possible. The
`"sample"`

method gives the sample skewness of the distribution.

…

arguments to be passed.

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

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

# NOT RUN { ## mean - ## var - # Mean, Variance: r = rnorm(100) mean(r) var(r) ## skewness - skewness(r) data(managers) skewness(managers) # }