compute skewness of a univariate distribution.
1 |
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 |
... |
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) = sum((x-mean(x))^3/var(x)^(3/2))/length(x)
skewness(sample) = sum(((x-mean(x))/var(x))^3)*n/((n-1)*(n-2))
Skewness(fisher)((sqrt(n*(n-1))/(n-2))*(sum(x^3)/n))/((sum(x^2)/n)^(3/2))
where n is the number of return, \overline{r} is the mean of the return distribution, σ_P is its standard deviation and σ_{S_P} is its sample standard deviation
Diethelm Wuertz, Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.83-84
kurtosis
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