On the Asymptotic Behavior of Sums of Order Statistics from a Distribution with a Slowly Varying Upper Tail

• Erich Haeusler
• David M. Mason
Chapter
Part of the Progress in Probability book series (PRPR, volume 23)

Abstract

Let (X n)n≥1 be a sequence of independent non-negative random variables from a common distribution function F with a regiilarly varying upper tail. A number of results are presented on the stability, asymptotic distribution and law of the iterated logarithm for trimmed sums formed by deleting a number of the upper extreme values from the partial sum X 1 +...+X n at each stage n. The methods of proof are entirely based on quantile function techniques. This paper should provide the reader with a good introduction to some of the possibilities and the scope of this methodology.

Keywords

Asymptotic Distribution Empirical Process Iterate Logarithm Empirical Distribution Function Common Distribution Function

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