Skewness

See also: Kurtosis (K), Statistical descriptions of model outputs

This is the degree to which the distribution is 'lopsided'. A positive skewness means a longer right tail; a negative skewness means a longer left tail. Zero skewness means the distribution is symmetric about its mean.

The skewness (S) is calculated as:

The s3 factor is put in to make the skewness a pure number i.e. it has no units of measurement. Skewness is also known as the third moment about the mean (with the symbol 3) and is even more sensitive to the data points in the tails of a distribution than the variance or standard deviation because of the cubed term.

Another measure of skewness, though rarely used, is the percentile skewness Sp, calculated as:

 

It has the advantage over the standard skewness of being quite stable because it is not affected by the values of the extreme data points. However, its scaling is different to standard skewness:

If:   

  • 0 < Sp < 1 the distribution is negatively skewed

  • Sp = 1 the distribution is symmetric

  • Sp > 1 the distribution is positively skewed

Read on: Kurtosis (K)

 

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