Indices of Skewness and Kurtosis - Indices of Univariate Skewness

The sample mean and variance for the jth variable xj are defined in the standard fashion as

(171)

and

(172)

Uncorrected univariate skewness. The uncorrected univariate skewness for variable xj is defined as

(173)

Corrected univariate skewness. The uncorrected estimate is biased. The following corrected univariate skewness is an unbiased estimate when the distribution is normal.

(174)

The asymptotic variance of these measures is 6/N, which is used to standardize the uncorrected skewness to produce the "normalized" skewness printed by the program.