On tail behaviour of kth upper order statistics under fixed and random sample sizes via tail equivalence

Ravi, S. and Manohar, M. C. (2018) On tail behaviour of kth upper order statistics under fixed and random sample sizes via tail equivalence. Statistics: A Journal of Theoretical and Applied Statistics, 52 (1). pp. 156-176. ISSN 0233-1888

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Abstract

For a fixed positive integer k, limit laws of linearly normalized kth upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized kth 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.

Item Type:	Article
Subjects:	E Mathematical Science > Statistics
Divisions:	Department of > Statistics
Depositing User:	Manjula P Library Assistant
Date Deposited:	16 Jul 2019 09:45
Last Modified:	16 Jul 2019 09:45
URI:	http://eprints.uni-mysore.ac.in/id/eprint/5267

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