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Nonparametric skew
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.〔Arnold BC, Groeneveld RA (1995) Measuring skewness with respect to the mode. The American Statistician 49 (1) 34–38 DOI:10.1080/00031305.1995.10476109〕〔Rubio F.J.; Steel M.F.J. (2012) "On the Marshall–Olkin transformation as a skewing mechanism". ''Computational Statistics & Data Analysis'' (Preprint )〕 It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean. Its calculation does not require any knowledge of the form of the underlying distribution—hence the name nonparametric. It has some desirable properties: it is zero for any symmetric distribution; it is
unaffected by a scale shift; and it reveals either left- or right-skewness equally well. Although its use has been mentioned in older textbooks〔Yule G.U.; Kendall M.G. (1950) ''An Introduction to the Theory of Statistics''. 3rd edition. Harper Publishing Company pp 162–163〕〔Hildebrand DK (1986) Statistical thinking for behavioral scientists. Boston: Duxbury〕 it appears to have gone out of fashion. In statistical samples it has been shown to be less powerful〔Tabor J (2010) Investigating the Investigative Task: Testing for skewness - An investigation of different test statistics and their power to detect skewness. J Stat Ed 18: 1–13〕 than the usual measures of skewness in detecting departures of the population from normality.〔
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