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.

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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
Subjects:	E Mathematical Science > Statistics
Divisions:	Department of > Statistics
Depositing User:	Arshiya Kousar Library Assistant
Date Deposited:	21 Aug 2019 08:18
Last Modified:	21 Aug 2019 08:18
URI:	http://eprints.uni-mysore.ac.in/id/eprint/4381

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