Extensions of true skewness for unimodal distributions

09/22/2022

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by   Yevgeniy Kovchegov, et al.

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A 2022 paper arXiv:2009.10305v4 introduced the notion of true positive and negative skewness for continuous random variables via Fréchet p-means. In this work, we find novel criteria for true skewness, establish true skewness for the Weibull, Lévy, skew-normal, and chi-squared distributions, and discuss the extension of true skewness to discrete and multivariate settings. Furthermore, some relevant properties of the p-means of random variables are established.