Quantifying closeness of distributions of sums and maxima when tails are fat

E.K.E. Willekens, S.I. Resnick

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Let X1, X2,…, Xn be n independent, identically distributed, non negative random variables and put and Mn = ni=1 Xi. Let (X, Y) denote the uniform distanc distributions of random variables X and Y; i.e.We consider (Sn, Mn) when P(X1>x) is slowly varying and we provide bounds for the asymptotic behaviour of this quantity as n¿8, thereby establishing a uniform rate of convergence result in Darling's law for distributions with slowly varying tails.
Original languageEnglish
Pages (from-to)201-216
JournalStochastic Processes and their Applications
Volume33
Issue number2
DOIs
Publication statusPublished - 1989

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