On tail behaviour of kth upper order statistics under fixed and random sample sizes via tail equivalence. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Ravi, Sreenivasan; Manohar, Mandagere Chandrashekhar
• Is Part Of: Statistics. Volume 52:Issue 1(2018)
• Page Start: 156
• Page End: 176
• Publication Date: 2018-01-02
• Subjects: Tail behaviour -- tail equivalence -- kth extremes -- partial maxima -- max domains of attraction -- stochastic ordering -- Burr distribution; 60F10; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1335316
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: For a fixed positive integer k, limit laws of linearly normalized k th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized k th upper order statistics under fixed and random sample sizes is carried out using tail equivalence which leads to some interesting tail behaviours of the limit laws. These lead to definitive answers about their max domains of attraction. Stochastic ordering properties of the limit laws are also studied. The results obtained are not dependent on linear norming and apply to power norming as well and generalize some results already available in the literature. And the proofs given here are elementary.