Bounded Distributions place Limits on Skewness and Larger Moments

08/09/2023

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by   David J Meer, et al.

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Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness D_3 is bounded from below by a function of the coefficient of variation (CoV) δ as D_3 ≥δ-1/δ. The results are extended to any distribution that is bounded with minimum value x_ min and/or bounded with maximum value x_ max. We build on the results to provide bounds for kurtosis D_4, and conjecture analogous bounds exists for higher statistical moments.