### Asymptotic Distributions and Berry-Esseen Bounds for Sums of Record Values

Qi-Man Shao (University of Oregon and National University of Singapore)
Chun Su (University of Science an Technology of China)
Gang Wei (Hong Kong Baptist University)

#### Abstract

Let $\{U_n, n \geq 1\}$ be independent uniformly distributed random variables, and $\{Y_n, n \geq 1\}$ be independent and identically distributed non-negative random variables with finite third moments. Denote $S_n = \sum_{i=1}^n Y_i$ and assume that $(U_1, \cdots, U_n)$ and $S_{n+1}$ are independent for every fixed $n$. In this paper we obtain Berry-Esseen bounds for $\sum_{i=1}^n \psi(U_i S_{n+1})$, where $\psi$ is a non-negative function. As an application, we give Berry-Esseen bounds and asymptotic distributions for sums of record values.

Pages: 544-559

Publication Date: June 25, 2004

DOI: 10.1214/EJP.v9-210

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