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On Some Models of Ordered Random Variables and Characterizations of Distributions

Abstract

The concept of extended neighboring order statistics introduced in Asadi et al. (2001) is a general model containing models of ordered random variables that are included in the generalized order statistics. This model also includes several models of ordered random variables that are not included in the generalized order statistics and is a helpful tool in unifying characterization results from several models of ordered random variables. In this paper, some general classes of distributions with many applications in reliability analysis and engineering, such as negative exponential, inverse exponential, Pareto, negative Pareto, inverse Pareto, power function, negative power, beta of the first kind, rectangular, Cauchy, Raleigh, Lomax, etc., have been characterized by using the regression of extended neighboring order statistics and decreasingly ordered random variables.

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ACKNOWLEDGMENTS

The authors would like to thank Associate Editor and two anonymous referees for their constructive comments and suggestions which improved the presentation of the paper.

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Correspondence to Mahdi Tavangar or Ismihan Bayramoglu.

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Tavangar, M., Bayramoglu, I. On Some Models of Ordered Random Variables and Characterizations of Distributions. Math. Meth. Stat. 29, 149–158 (2020). https://doi.org/10.3103/S1066530720030035

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  • DOI: https://doi.org/10.3103/S1066530720030035

Keywords:

  • characterizations of distributions
  • order statistics
  • extended neighboring order statistics
  • generalized order statistics
  • regression of order statistics