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A New Life of Pearson’s Skewness

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  • Yevgeniy Kovchegov

    (Oregon State University)

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.

Suggested Citation

  • Yevgeniy Kovchegov, 2022. "A New Life of Pearson’s Skewness," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2896-2915, December.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:4:d:10.1007_s10959-021-01149-7
    DOI: 10.1007/s10959-021-01149-7
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    References listed on IDEAS

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    1. W. R. van Zwet, 1964. "Convex transformations: A new approach to slcewness and kurtosis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 18(4), pages 433-441, December.
    2. Abadir, Karim M., 2005. "The Mean-Median-Mode Inequality: Counterexamples," Econometric Theory, Cambridge University Press, vol. 21(2), pages 477-482, April.
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