• On the Limit Distribution of Lower Extreme Generalized Order Statistics

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      https://www.ias.ac.in/article/fulltext/pmsc/122/02/0297-0311

    • Keywords

       

      Weak convergence; generalized order statistics; extreme value theory; order statistics; progressive Type II censored order statistics.

    • Abstract

       

      In a wide subclass of generalized order statistics $(gOs)$, which contains most of the known and important models of ordered random variables, weak convergence of lower extremes are developed. A recent result of extreme value theory of $m-gOs$ (as well as the classical extreme value theory of ordinary order statistics) yields three types of limit distributions that are possible in case of linear normalization. In this paper a similar classification of limit distributions holds for extreme $gOs$, where the parameters $\gamma_j,j=1,\ldots,n$, are assumed to be pairwise different. Two illustrative examples are given to demonstrate the practical importance for some of the obtained results.

    • Author Affiliations

       

      H M Barakat1 Magdy E El-Adll2

      1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
      2. Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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