Research article

Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables

  • Received: 26 August 2020 Accepted: 08 October 2020 Published: 22 October 2020
  • MSC : Primary 90B25; Secondary 60E15, 60K10

  • In this paper, we carry out stochastic comparisons on extreme order statistics (i.e. smallest and largest order statistics) from dependent and heterogeneous samples following modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models. We build the usual stochastic order for sample minimums and maximums, and the hazard rate order on minimums of sample and the reversed hazard rate order on maximums of sample are also derived, respectively. Finally, some examples are given to illustrate the theoretical results.

    Citation: Miaomiao Zhang, Bin Lu, Rongfang Yan. Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables[J]. AIMS Mathematics, 2021, 6(1): 584-606. doi: 10.3934/math.2021036

    Related Papers:

  • In this paper, we carry out stochastic comparisons on extreme order statistics (i.e. smallest and largest order statistics) from dependent and heterogeneous samples following modified proportional hazard rates (MPHR) and modified proportional reversed hazard rates (MPRHR) models. We build the usual stochastic order for sample minimums and maximums, and the hazard rate order on minimums of sample and the reversed hazard rate order on maximums of sample are also derived, respectively. Finally, some examples are given to illustrate the theoretical results.


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