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 Un, n >= 1 be independent uniformly distributed
random variables, and Yn, n >= 1 be independent and
identically distributed non-negative random variables with finite third
moments. Denote Sn the partial sum of Yi
and assume that (U1, ..., Un) and Sn+1
are independent for every
fixed n. In this paper we obtain Berry-Esseen bounds for
the partial sum of g(Ui Sn+1), where g is a non-negative
function. As an application, we give Berry-Esseen bounds and asymptotic
distributions for sums of record values.
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