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Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables

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Listed:
  • Longxiang Fang
  • Narayanaswamy Balakrishnan
  • Wenyu Huang
  • Shuai Zhang

Abstract

In this paper, we discuss stochastic comparison of the largest order statistics arising from two sets of dependent distribution‐free random variables with respect to multivariate chain majorization, where the dependency structure can be defined by Archimedean copulas. When a distribution‐free model with possibly two parameter vectors has its matrix of parameters changing to another matrix of parameters in a certain mathematical sense, we obtain the first sample maxima is larger than the second sample maxima with respect to the usual stochastic order, based on certain conditions. Applications of our results for scale proportional reverse hazards model, exponentiated gamma distribution, Gompertz–Makeham distribution, and location‐scale model, are also given. Meanwhile, we provide two numerical examples to illustrate the results established here.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:77:y:2023:i:1:p:99-112
    DOI: 10.1111/stan.12275
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    References listed on IDEAS

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    1. Crescenzo, Antonio Di, 2000. "Some results on the proportional reversed hazards model," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 313-321, December.
    2. 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.
    3. Paulo Oliveira & Nuria Torrado, 2015. "On proportional reversed failure rate class," Statistical Papers, Springer, vol. 56(4), pages 999-1013, November.
    4. Li, Xiaohu & Fang, Rui, 2015. "Ordering properties of order statistics from random variables of Archimedean copulas with applications," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 304-320.
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