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

E. Willekens and S. I. Resnick

Stochastic Processes and their Applications, 1989, vol. 33, issue 2, 201-216

Abstract: Let X1, X2,..., Xn be n independent, identically distributed, non negative random variables and put and Mn = [logical and operator]ni=1 Xi. Let [varrho](X, Y) denote the uniform distanc distributions of random variables X and Y; i.e. . We consider [varrho](Sn, Mn) when P(X1>x) is slowly varying and we provide bounds for the asymptotic behaviour of this quantity as n-->[infinity], thereby establishing a uniform rate of convergence result in Darling's law for distributions with slowly varying tails.

Keywords: slow; variation; partial; sums; partial; maxima (search for similar items in EconPapers)
Date: 1989
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