On the number and sum of near-record observations
N. Balakrishnan, A.G. Pakes, and A. Stepanov
Source: Adv. in Appl. Probab. Volume 37, Number 3
(2005), 765-780.
Abstract
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.
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Keywords: Record; near-record observation; record time; sum of near-record observations; insurance claim; limit theorem
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1127483746
Digital Object Identifier: doi:10.1239/aap/1127483746
Mathematical Reviews number (MathSciNet): MR2156559
Zentralblatt MATH identifier: 1080.60053
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