A New Life of Pearson’s Skewness

Yevgeniy Kovchegov ()
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Yevgeniy Kovchegov: Oregon State University

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2896-2915

Abstract: Abstract In this work, we show how coupling and stochastic dominance methods can be successfully applied to a classical problem of rigorizing Pearson’s skewness. Here, we use Fréchet means to define generalized notions of positive and negative skewness that we call truly positive and truly negative. Then, we apply a stochastic dominance approach in establishing criteria for determining whether a continuous random variable is truly positively skewed. Intuitively, this means that the scaled right tail of the probability density function exhibits strict stochastic dominance over the equivalently scaled left tail. Finally, we use the stochastic dominance criteria and establish some basic examples of true positive skewness, thus demonstrating how the approach works in general.

Keywords: Skewness; Fréchet mean; Stochastic dominance; Coupling method; Centroids; 60E15; 62A99 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01149-7

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