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On a Time Dependent Divergence Measure between Two Residual Lifetime Distributions

Abstract

Recently, a time-dependent measure of divergence has been introduced by Mansourvar and Asadi (2020) to assess the discrepancy between the survival functions of two residual lifetime random variables. In this paper, we derive various time-dependent results on the proposed divergence measure in connection to other well-known measures in reliability engineering. The proposed criterion is also examined in mixture models and a general class of survival transformation models which results in some well-known models in the lifetime studies and survival analysis. In addition, the time-dependent measure is employed to evaluate the divergence between the lifetime distributions of \(k\)-out-of-\(n\) systems and also to assess the discrepancy between the distribution functions of the epoch times of a non-homogeneous Poisson process.

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ACKNOWLEDGMENTS

The authors would like to thank the Associate Editor and two reviewers for their constructive comments that greatly improved the paper.

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The authors declare that they have no conflict of interest.

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Correspondence to Zahra Mansourvar or Majid Asadi.

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Mansourvar, Z., Asadi, M. On a Time Dependent Divergence Measure between Two Residual Lifetime Distributions. Math. Meth. Stat. 29, 135–148 (2020). https://doi.org/10.3103/S1066530720030023

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  • DOI: https://doi.org/10.3103/S1066530720030023

Keywords:

  • aging properties
  • divergence measures
  • ordered random variables
  • residual lifetime distributions
  • survival transformation model