Comparisons of series and parallel systems with heterogeneous exponentiated geometric components

Ghobad Barmalzan and Somayeh Shahraki Dehsukhteh

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 18, 4352-4366

Abstract: This article examines the problem of stochastic comparisons of series and parallel systems with independent heterogeneous exponentiated geometric (EG) components. Suppose X1,…,Xn and Y1,…,Yn are independent non negative random variables with Xi∼EG(αi,pi) and Yi∼EG(αi*,pi*). In this article, we present under some restrictions on the involved parameters that Xn:n is greater than Yn:n with respect to the usual stochastic order, when α* is weakly supermajorized by α, and − log(1−p*) is weakly supermajorized by − log(1−p). We also establish the usual stochastic order between Xn:n and Yn:n by using the unordered majorization between α and α*, and the p-majorization order between − log(1−p) and − log(1−p*). For the series systems, in the case αi=αi*≤1,i=1,…,n and some restrictions on the involved parameters, we establish X1:n is greater than Y1:n with respect to the usual stochastic order, when − log(1−p*) is weakly supermajorized by − log(1−p). On the other hand, sufficient conditions are given for the comparison of X1:n and Y1:n, when logα* is weakly submajorized by logα.

Date: 2021
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DOI: 10.1080/03610926.2020.1716251

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