1 Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand 2 School of Mathematics, University of Manchester, Manchester M13 9PL, UK
Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 687-690.
Soit X une variable aléatoire, les moments vérifient :
Si , alors pour , il existe une variable aléatoire telle que
On applique l'inégalité à pour obtenir de nouvelles inégalités sur les moments lorsque . On applique le résultat à l'obtention de bornes plus précises du coefficient de dissymétrie et du coefficient d'applatissement.
Given a random variable X, the moments, , satisfy
for . If , then for , there is a random variable such that
for . We apply the inequality to to obtain new inequalities for the moments when . An application is illustrated to obtain tighter bounds for skewness and kurtosis.
Christopher S. Withers 1 ;
Saralees Nadarajah 2
1 Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand 2 School of Mathematics, University of Manchester, Manchester M13 9PL, UK
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author = {Christopher S. Withers and Saralees Nadarajah},
title = {Moment inequalities for positive random variables},
journal = {Comptes Rendus. Math\'ematique},
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year = {2010},
doi = {10.1016/j.crma.2010.04.014},
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Christopher S. Withers; Saralees Nadarajah. Moment inequalities for positive random variables. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 687-690. doi : 10.1016/j.crma.2010.04.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.014/
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[3] T. Artikis; A. Voudouri Limiting behaviour of certain mixtures of distributions, Analysis Mathematica, Volume 16 (1990), pp. 81-86