# The Quantile-Transform-Empirical-Process Approach to Limit Theorems for Sums of Order Statistics

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

## Abstract

Let X, X 1, X 2,..., be independent, real-valued non-degenerate random variables with the common distribution function F(x) = P{Xx}, xR, and introduce the inverse or quantile function Q of F define as
$$Q(s) = \inf \{ x:F(x) \ge s\} ,\,\,0 < s \le 1,\,\,Q(0) = Q(0 + ).$$

## Keywords

Order Statistic Asymptotic Distribution Asymptotic Normality Iterate Logarithm Quantile Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Sándor Csörgő
• 1
• Erich Haeusler
• 2
• David M. Mason
• 3
1. 1.Department of StatisticsUniversity of MichiganAnn ArborUSA
2. 2.University of MunichMunich 2West Germany
3. 3.Department of Mathematical SciencesUniversity of DelawareNewarkUSA