Bounded distributions place limits on skewness and larger moments.

Abstract

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 D3 is bounded from below by a function of the coefficient of variation (CoV) δ as D3 > δ - 1/δ. The results are extended to any distribution that is bounded with minimum value xmin and/or bounded with maximum value xmax. We build on the results to provide bounds for kurtosis D4, and conjecture analogous bounds exists for higher statistical moments.