Stochastic comparisons of second-order statistics from dependent and heterogeneous modified proportional (reversed) hazard rates scale models

Bin Lu; Bin Lu

doi:10.3934/math.2024434

AIMS Mathematics

2024, Volume 9, Issue 4: 8904-8919. doi: 10.3934/math.2024434

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Research article

Stochastic comparisons of second-order statistics from dependent and heterogeneous modified proportional (reversed) hazard rates scale models

Bin Lu ^,

Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received: 02 November 2023 Revised: 21 February 2024 Accepted: 22 February 2024 Published: 04 March 2024
MSC : Primary 90B25, Secondary 60E15, 60K10

In this paper, we investigate the problem of stochastically comparing the second-order statistics from dependent and heterogeneous samples following modified proportional hazard rates scale (MPHRS) and modified proportional reversed hazard rates scale (MPRHRS) models under Archimedean copula. We built some sufficient conditions for the usual stochastic order whenever the samples have different parameter vectors. Finally, some numerical examples were provided to illustrate the theoretical results.
- second-order statistics,
- MPHRS and MPRHRS models,
- archimedean copula,
- majorization
Citation: Bin Lu. Stochastic comparisons of second-order statistics from dependent and heterogeneous modified proportional (reversed) hazard rates scale models[J]. AIMS Mathematics, 2024, 9(4): 8904-8919. doi: 10.3934/math.2024434

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Abstract

In this paper, we investigate the problem of stochastically comparing the second-order statistics from dependent and heterogeneous samples following modified proportional hazard rates scale (MPHRS) and modified proportional reversed hazard rates scale (MPRHRS) models under Archimedean copula. We built some sufficient conditions for the usual stochastic order whenever the samples have different parameter vectors. Finally, some numerical examples were provided to illustrate the theoretical results.

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