Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 621-630.

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Stochastic Ordering of Sample Minima from Scale Proportional Hazards Random Variables Under Archimedean Copula Dependence

Longxiang Fang1,*(),Balakrishnan Narayanaswamy2,Wenyu Huang1   

  1. 1 Department of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241002
    2 Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
  • Received:2020-02-06 Online:2022-04-26 Published:2022-04-18
  • Contact: Longxiang Fang E-mail:lxfang@fudan.edu.cn
  • Supported by:
    the Anhui Provincial Philosophy and Social Science Planning Fund(AHSKF2021D30)

Abstract:

In this paper, we discuss stochastic comparisons of the smallest order statistics arising from two sets of dependent scale proportional hazards random variables with respect to multivariate chain majorization. When a scale proportional hazards model with possibly different frailty and scale parameters has its matrix of parameters changing to another matrix of parameters in a certain mathematical sense, we study the first sample minimum is less than the second minimum with respect to the usual stochastic order, based on certain conditions. Some examples are also presented for illustrating the results established here.

Key words: Archimedean copula, Usual stochastic order, Scale proportional hazards model, Multivariate chain majorization

CLC Number: 

  • O211.9
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