Bounded distributions place limits on skewness and larger moments Article Swipe

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Skewness Kurtosis Bounded function Standard deviation Mathematics Statistics Conjecture Distribution (mathematics) Function (biology) Combinatorics Mathematical analysis Evolutionary biology Biology

D. Meer , Eric R. Weeks ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1371/journal.pone.0297862 · OA: W4391677775

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.