Stochastic Comparisons of Parallel Systems of Heterogeneous Generalized Exponential Components

Amarjit Kundu, Shovan Chowdhury () and Asok K Nanda
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Amarjit Kundu: Santipur College
Shovan Chowdhury: Indian Institute of Management Kozhikode
Asok K Nanda: Indian Institute of Science and Educational Research

No 162, Working papers from Indian Institute of Management Kozhikode

Abstract: Let X1, X2, . . . , Xn (resp. Y1, Y2, . . . , Yn) be independent random variables such that Xi (resp. Yi) follows generalized exponential distribution with shape parameter ?i and scale parameter ?i (resp. ?i), i = 1, 2, . . . , n. Here it is shown that if ? = (?1, ?2, . . . , ?n) majorizes ? = (?1, ?2, . . . , ?n) then Xn:n will be greater than Yn:n in reversed hazard rate ordering. That no relation exists between Xn:n and Yn:n, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if Yi follows generalized exponential distribution with parameters ?, ?i , where ? is the mean of all ?i ’s, i = 1 . . . n, then Xn:n is greater than Yn:n in likelihood ratio ordering. In this context, an error in Marshall, Olkin and Arnold [Inequalities: Theory of Majorization and Its applications(2011)] has been corrected, and some new results on majorization have been developed.

Keywords: Hazard rate function; majorization; reversed hazard rate function; Schur-convex and Schur-concave functions; stochastic orders. (search for similar items in EconPapers)
Pages: 18 pages
Date: 2014
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