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


  • Willekens, E.
  • Resnick, S. I.


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.

Suggested Citation

  • Willekens, E. & Resnick, S. I., 1989. "Quantifying closeness of distributions of sums and maxima when tails are fat," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 201-216, December.
  • Handle: RePEc:eee:spapps:v:33:y:1989:i:2:p:201-216

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    Cited by:

    1. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, Tinbergen Institute.


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