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On the number and sum of near-record observations

Part of: Nonparametric inference Stochastic processes

Published online by Cambridge University Press:  01 July 2016

N. Balakrishnan ,
A.G. Pakes  and
A. Stepanov
N. Balakrishnan*
Affiliation:
McMaster University
A.G. Pakes*
Affiliation:
The University of Western Australia
A. Stepanov*
Affiliation:
Kaliningrad State Technical University
*
∗ Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada. Email address: bala@univmail.cis.mcmaster.ca
∗∗ Postal address: Department of Mathematics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. Email address: pakes@maths.uwa.edu.au
∗∗∗ Postal address: Department of Mathematics, Kaliningrad State Technical University, Sovietsky Prospect 1, Kaliningrad, 236000, Russia. Email address: alexei@step.koenig.ru
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Abstract

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Let X1,X2,… be a sequence of independent and identically distributed random variables with some continuous distribution function F. Let L(n) and X(n) denote the nth record time and the nth record value, respectively. We refer to the variables Xi as near-nth-record observations if Xi∈(X(n)-a,X(n)], with a>0, and L(n)<i<L(n+1). In this work we study asymptotic properties of the number of near-record observations. We also discuss sums of near-record observations.

Keywords

Recordnear-record observationrecord timesum of near-record observationsinsurance claimlimit theorem

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G30: Order statistics; empirical distribution functions
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 3 , September 2005 , pp. 765 - 780
Copyright
Copyright © Applied Probability Trust 2005 

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