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Pearson Mode Skewness

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

(mean-mode)/sigma.

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

(mean-mode)/sigma=1/2alpha_3,

where alpha_3 is the third standardized moment (Kenney and Keeping 1962, p. 101; Kenney and Keeping 1951, p. 106).

See also

Bowley Skewness, Mean, Mode, Pearson's Skewness Coefficients, Skewness

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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.

Referenced on Wolfram|Alpha

Pearson Mode Skewness

Cite this as:

Weisstein, Eric W. "Pearson Mode Skewness." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PearsonModeSkewness.html

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