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ON SKEWNESS AND DISPERSION AMONG CONVOLUTIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

Published online by Cambridge University Press:  02 November 2010

Leila Amiri
Affiliation:
Department of Statistics, Razi University, Kermanshah, Iran E-mail: bkhaledi@hotmail.com
Baha-Eldin Khaledi
Affiliation:
Department of Statistics, Razi University, Kermanshah, Iran E-mail: bkhaledi@hotmail.com
Francisco J. Samaniego
Affiliation:
Department of Statistics, University of California, Davis, CA
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Abstract

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Let {x(1)≤···≤x(n)} denote the increasing arrangement of the components of a vector x=(x1, …, xn). A vector xRn majorizes another vector y (written ) if for j = 1, …, n−1 and . A vector xR+n majorizes reciprocally another vector yR+n (written ) if for j = 1, …, n. Let , be n independent random variables such that is a gamma random variable with shape parameter α≥1 and scale parameter λi, i = 1, …, n. We show that if , then is greater than according to right spread order as well as mean residual life order. We also prove that if , then is greater than according to new better than used in expectation order as well as Lorenze order. These results mainly generalize the recent results of Kochar and Xu [7] and Zhao and Balakrishnan [14] from convolutions of independent exponential random variables to convolutions of independent gamma random variables with common shape parameters greater than or equal to 1.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2011

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