• On the Limit Distribution of Lower Extreme Generalized Order Statistics

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019