On the Limit Distribution of Lower Extreme Generalized Order Statistics

Proceedings Mathematical Sciences

Magdy E El-Adll¹  H M Barakat² 

[1] Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt$$;Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt$$

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

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $𝛾_j,j=1,ldots,n$, are assumed to be pairwise different. Two illustrative examples are given to demonstrate the practical importance for some of the obtained results.

【 授权许可】

Unknown