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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 ,
Baha-Eldin Khaledi  and
Francisco J. Samaniego
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

Let {x(1)≤···≤x(n)} denote the increasing arrangement of the components of a vector x=(x1, …, xn). A vector x∈Rn majorizes another vector y (written ) if for j = 1, …, n−1 and . A vector x∈R+n majorizes reciprocally another vector y∈R+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
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 1 , January 2011 , pp. 55 - 69
Copyright
Copyright © Cambridge University Press 2011

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