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Abstract <p>A distributional identity for generalized order statistics is presented in two versions along with a characterization of exponential and Pareto distributions, respectively, under mild conditions. In its multiplicative form, the identity extends previous random dilation results in models of ordered random variables. The relations can be utilized as a statistical method to predict future generalized order statistics or other quantities of interest within submodels.</p>

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A Distributional Identity for Generalized Order Statistics with Characterizations Useful for Prediction

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Mahdi Alimohammadi,
  • Udo Kamps,
  • Fariba Azizi,
  • Marziyeh Pourbagher

摘要

Abstract

A distributional identity for generalized order statistics is presented in two versions along with a characterization of exponential and Pareto distributions, respectively, under mild conditions. In its multiplicative form, the identity extends previous random dilation results in models of ordered random variables. The relations can be utilized as a statistical method to predict future generalized order statistics or other quantities of interest within submodels.