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February 2020 Application of weighted and unordered majorization orders in comparisons of parallel systems with exponentiated generalized gamma components
Abedin Haidari, Amir T. Payandeh Najafabadi, Narayanaswamy Balakrishnan
Braz. J. Probab. Stat. 34(1): 150-166 (February 2020). DOI: 10.1214/18-BJPS410

Abstract

Consider two parallel systems, say $A$ and $B$, with respective lifetimes $T_{1}$ and $T_{2}$ wherein independent component lifetimes of each system follow exponentiated generalized gamma distribution with possibly different exponential shape and scale parameters. We show here that $T_{2}$ is smaller than $T_{1}$ with respect to the usual stochastic order (reversed hazard rate order) if the vector of logarithm (the main vector) of scale parameters of System $B$ is weakly weighted majorized by that of System $A$, and if the vector of exponential shape parameters of System $A$ is unordered mojorized by that of System $B$. By means of some examples, we show that the above results can not be extended to the hazard rate and likelihood ratio orders. However, when the scale parameters of each system divide into two homogeneous groups, we verify that the usual stochastic and reversed hazard rate orders can be extended, respectively, to the hazard rate and likelihood ratio orders. The established results complete and strengthen some of the known results in the literature.

Citation

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Abedin Haidari. Amir T. Payandeh Najafabadi. Narayanaswamy Balakrishnan. "Application of weighted and unordered majorization orders in comparisons of parallel systems with exponentiated generalized gamma components." Braz. J. Probab. Stat. 34 (1) 150 - 166, February 2020. https://doi.org/10.1214/18-BJPS410

Information

Received: 1 March 2018; Accepted: 1 July 2018; Published: February 2020
First available in Project Euclid: 3 February 2020

zbMATH: 07200397
MathSciNet: MR4058976
Digital Object Identifier: 10.1214/18-BJPS410

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 1 • February 2020
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