On the asymptotic behaviour of extremes and near maxima of random observations from the general error distributions

Vasudeva, R. and Vasantha Kumari, J. and Ravi, S. (2014) On the asymptotic behaviour of extremes and near maxima of random observations from the general error distributions. Journal of Applied Probability, 51 (2). pp. 528-541. ISSN 0021-9002

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Official URL: http://dx.doi.org/10.1239/jap/1402578641

Abstract

As the name suggests, the family of general error distributions has been used to model nonnormal errors in a variety of situations. In this article we show that the asymptotic distribution of linearly normalized partial maxima of random observations from the general error distributions is Gumbel when the parameter of these distributions lies in the interval (0, 1). Our result fills a gap in the literature. We also establish the corresponding density convergence, obtain an asymptotic distribution of the partial maxima under power normalization, and state and prove a strong law. We also study the asymptotic behaviour of observations near the partial maxima and the sum of such observations.

Item Type: Article
Additional Information: Unmapped bibliographic data: LA - en [Field not mapped to EPrints] J2 - J. Appl. Probab. [Field not mapped to EPrints] VN - 51 [Field not mapped to EPrints]
Uncontrolled Keywords: Extremes, general error distribution, Gumbel distribution, strong law for partial maxima, near maxima, power normalization
Subjects: Physical Sciences > Statistics
Divisions: PG Campuses > Manasagangotri, Mysore > Statistics
Depositing User: Praveen Kumari B.L
Date Deposited: 24 Mar 2015 10:26
Last Modified: 24 Mar 2015 10:26
URI: http://eprints.uni-mysore.ac.in/id/eprint/17569

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