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Ordering results of the smallest and largest order statistics from independent heterogeneous exponentiated gamma random variables

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  • Longxiang Fang
  • Tingtao Xu

Abstract

In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous exponentiated gamma components. The results established here are developed in two directions. First, when a system possibly has different shape and scale parameters and the matrix of those different parameters following the chain majorization order, we study the reversed hazard rate order of parallel systems and the usual stochastic order of series systems. Next, by using the concept of vector majorization, we establish the usual stochastic order of series systems and the reversed hazard rate order of parallel systems.

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  • Longxiang Fang & Tingtao Xu, 2019. "Ordering results of the smallest and largest order statistics from independent heterogeneous exponentiated gamma random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(2), pages 197-210, May.
    • Handle: RePEc:bla:stanee:v:73:y:2019:i:2:p:197-210
    DOI: 10.1111/stan.12164
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    Cited by:

    1. Longxiang Fang & Narayanaswamy Balakrishnan & Wenyu Huang & Shuai Zhang, 2023. "Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 99-112, February.

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