Pearson Mode Skewness

Given a statistical distribution with measured mean, mode, and standard deviation , the Pearson mode skewness is

The function was incorrectly implemented (with a spurious multiplicative factor of 3) in versions of the Wolfram Language prior to 6 as PearsonSkewness1[data] after loading the package Statistics`DescriptiveStatistics`.

This measure was suggested by Karl Pearson, and has the property that for a type III Pearson distribution, it is equal to

where  is the third standardized moment (Kenney and Keeping 1962, p. 101; Kenney and Keeping 1951, p. 106).

REFERENCES:

Hildebrand, D. K. Statistical Thinking for Behavioral Scientists. Boston: Duxbury, 1986.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, p. 101, 1962.

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, p. 106, 1951.