Journal of Applied Probability

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

R. Vasudeva, J. Vasantha Kumari, and S. Ravi

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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.

Article information

Source
J. Appl. Probab., Volume 51, Number 2 (2014), 528-541.

Dates
First available in Project Euclid: 12 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1402578641

Digital Object Identifier
doi:10.1239/jap/1402578641

Mathematical Reviews number (MathSciNet)
MR3217783

Zentralblatt MATH identifier
1305.60018

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory

Keywords
Extremes general error distribution Gumbel distribution strong law for partial maxima near maxima power normalization

Citation

Vasudeva, R.; Kumari, J. Vasantha; Ravi, S. On the asymptotic behaviour of extremes and near maxima of random observations from the general error distributions. J. Appl. Probab. 51 (2014), no. 2, 528--541. doi:10.1239/jap/1402578641. https://projecteuclid.org/euclid.jap/1402578641


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