What is it about?
Generalized order statistics (gos) was introduced by Kamps (1995), as a general framework for models of ordered random variables. Extend the results of Barakat and El-Shandidy (2004), we study in this paper the asymptotic behavior of general sequence of any upper m-generalized order statistics (m-gos, m>-1) and m-dual generalized order statistics (m-dgos, m>-1) (extreme, intermediate and central terms) , which are connected asymptotically with some regularly varying functions. Moreover, the limit distribution functions of m-gos, as well as m-dgos, with random indices, are obtained under general conditions.
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Why is it important?
In many biological, agricultural and some quality control problems, it is almost impossible to have a fixed sample size, because some observations always get lost for various reasons. However, random sample sizes naturally arise in such topics as sequential analysis, branching processes, damage models or rarefaction of point processes and records as maxima. Therefore, We studied in this paper the weak convergence of generalized order statistics with random indices under general conditions. The weak convergence results in this paper when the normalizing constants are not random.
Perspectives
Writing this article was a great pleasure as it has co-authors with whom I have had long standing collaborations. This article also lead to do several papers in generalized order statistics with random sample size in general case and ultimately to a greater involvement in generalized order statistics research.
Mohamed Abd Elgawad
Read the Original
This page is a summary of: Generalized-order statistics with random indices, Communication in Statistics- Theory and Methods, June 2017, Taylor & Francis,
DOI: 10.1080/03610926.2017.1342837.
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