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Distributions of strictly positive numbers are common and can becharacterized by standard statistical measures such as mean, standarddeviation, and skewness. We demonstrate that for these distributions theskewness $D_3$ is bounded from below by a function of the coefficient ofvariation (CoV) $\delta$ as $D_3 \ge \delta-1/\delta$. The results are extendedto any distribution that is bounded with minimum value $x_{\rm min}$ and/orbounded with maximum value $x_{\rm max}$. We build on the results to providebounds for kurtosis $D_4$, and conjecture analogous bounds exists for higherstatistical moments.

Bounded Distributions place Limits on Skewness and Larger Moments