Comptes Rendus
Moment inequalities for positive random variables
Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 687-690.

Given a random variable X, the moments, {mr=EXr}, satisfy

for r0. If X0, then for n1, there is a random variable Xn such that
for r0. We apply the inequality Dr0 to Xn to obtain new inequalities for the moments when X0. An application is illustrated to obtain tighter bounds for skewness and kurtosis.

Soit X une variable aléatoire, les moments {mr=EXr} vérifient :

Si X0, alors pour n1, il existe une variable aléatoire Xn telle que
On applique l'inégalité Dr0 à Xn pour obtenir de nouvelles inégalités sur les moments lorsque X0. On applique le résultat à l'obtention de bornes plus précises du coefficient de dissymétrie et du coefficient d'applatissement.

Published online:
DOI: 10.1016/j.crma.2010.04.014

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
     author = {Christopher S. Withers and Saralees Nadarajah},
     title = {Moment inequalities for positive random variables},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {687--690},
     publisher = {Elsevier},
     volume = {348},
     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.014},
     language = {en},
AU  - Christopher S. Withers
AU  - Saralees Nadarajah
TI  - Moment inequalities for positive random variables
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 687
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VL  - 348
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crma.2010.04.014
LA  - en
ID  - CRMATH_2010__348_11-12_687_0
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%A Saralees Nadarajah
%T Moment inequalities for positive random variables
%J Comptes Rendus. Mathématique
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%R 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.

[1] J. Shao Mathematical Statistics, Springer Verlag, New York, 2003

[2] A. Bulinski; A. Shashkin Limit Theorems for Associated Random Fields and Related Systems, World Scientific Publishing Company, Hackensack, New Jersey, 2007

[3] T. Artikis; A. Voudouri Limiting behaviour of certain mixtures of distributions, Analysis Mathematica, Volume 16 (1990), pp. 81-86

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