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The Asymptotic Distributions of Sums of Records

Authors:	Barry C. Arnold Jose′ A. Villasenor

Affiliation:	(1) University of California, Riverside, USA;(2) Colegio de Postgraduados, Montecillo, Mexico

Abstract:	LetX₁,X₂... be a sequence of i.i.d. random variables and let $X^{left( 0 right)} left( { = X_1 } right),X^{left( 1 right)} ,X^{left( 2 right)} ...$ be the associated (upper) record sequence. Resnick (1973) identified the class of all possible limit distributions for $X^{left( n right)} - b_n /a_n$ . Here we focus on sums of records, $T_n = sumnolimits_{j = 0}^n {X^{left( j right)} }$ . We describe three cases in which T_n can be normalized to have a non-trivial limiting distribution. The problem of identifying all possible limit laws for normalized sums of records remains open.

Keywords:	Beta records Gumbel records exponential records infinitely divisible distributions
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