Stochastic comparisons of series and parallel systems with dependent and heterogeneous Topp-Leone generated components

Li Zhang; Rongfang Yan; Li Zhang; Rongfang Yan

doi:10.3934/math.2021124

AIMS Mathematics

2021, Volume 6, Issue 3: 2031-2047. doi: 10.3934/math.2021124

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Research article

Stochastic comparisons of series and parallel systems with dependent and heterogeneous Topp-Leone generated components

Li Zhang ,
Rongfang Yan ^,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 14 September 2020 Accepted: 18 November 2020 Published: 07 December 2020
MSC : Primary 90B25; Secondary 60E15, 60K10

In this paper, we carry out stochastic comparisons of lifetimes of series and parallel systems with dependent heterogeneous Topp-Leone generated components. The usual stochastic order and the reversed hazard rate order are developed for the parallel systems with the help of vector majorization under Archimedean copula dependence, and the results for the usual stochastic order are also obtained for the series systems. Finally, some numerical examples are provided to illustrate the effectiveness of our theoretical findings.
- stochastic orders,
- order statistics,
- majorization,
- Archimedean copula,
- Topp-Leone generated distribution
Citation: Li Zhang, Rongfang Yan. Stochastic comparisons of series and parallel systems with dependent and heterogeneous Topp-Leone generated components[J]. AIMS Mathematics, 2021, 6(3): 2031-2047. doi: 10.3934/math.2021124

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Abstract

In this paper, we carry out stochastic comparisons of lifetimes of series and parallel systems with dependent heterogeneous Topp-Leone generated components. The usual stochastic order and the reversed hazard rate order are developed for the parallel systems with the help of vector majorization under Archimedean copula dependence, and the results for the usual stochastic order are also obtained for the series systems. Finally, some numerical examples are provided to illustrate the effectiveness of our theoretical findings.

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