Bounded Distributions place Limits on Skewness and Larger Moments

Autor: Meer, David J, Weeks, Eric R.
Rok vydání: 2023
Předmět:
Zdroj: PLOS ONE 19, e0297862 (2024)
Druh dokumentu: Working Paper
DOI: 10.1371/journal.pone.0297862
Popis: 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) $\delta$ as $D_3 \ge \delta-1/\delta$. The results are extended to any distribution that is bounded with minimum value $x_{\rm min}$ and/or bounded with maximum value $x_{\rm max}$. We build on the results to provide bounds for kurtosis $D_4$, and conjecture analogous bounds exists for higher statistical moments.
Comment: 14 pages, 2 figures. Awaiting publication in PLoS One
Databáze: arXiv
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje