# skewness

##### Skewness

compute skewness of a univariate distribution.

##### Usage

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

##### Arguments

- 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.

##### 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

##### See Also

##### Examples

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

*Documentation reproduced from package PerformanceAnalytics, version 2.0.4, License:*