Skewness

Skewness(x, i, w)

Computes an estimate of the weighted skewness of a distribution, as given by

[math]\displaystyle{ \sum_i w_i \left({x-\bar{x}}\over\sigma\right)^3 / \sum_i w_i }[/math]

A symmetric distribution as zero skew. A distribution with a heavy right tail (like Gamma, LogNormal) is positively skewed. A distribution with a heavy left tail has a negative skew.

If one or more infinite values occur in x, the Skewness will be +INF, -INF or NAN. If min(x)=INF or max(x)=-INF, then skew=NAN. If min(x)=-INF and max(x)=INF then SKEW=NAN. If min(x)>-INF and max(x)=INF, then skew is +INF, and if min(x)=-INF, max(x)<INF, skew is -INF.

See also

• Statistical Functions and Importance Weighting