compute skewness of a univariate distribution.
skewness(x, na.rm = FALSE, method = c("moment", "fisher", "sample"), ...)a numeric vector or object.
a logical. Should missing values be removed?
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
## mean -
## var -
# Mean, Variance:
r = rnorm(100)
mean(r)
#> [1] -0.1833293
var(r)
#> [1] 1.214234
## skewness -
skewness(r)
#> [1] 0.105112
data(managers)
skewness(managers)
#> HAM1 HAM2 HAM3 HAM4 HAM5 HAM6
#> Skewness -0.6588445 1.45804 0.7908285 -0.4310631 0.07380869 -0.2799993
#> EDHEC LS EQ SP500 TR US 10Y TR US 3m TR
#> Skewness 0.01773013 -0.5531032 -0.4048722 -0.328171