Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics
نویسندگان
چکیده
Let X(i) < • • • < X(^) be the order statistics from n independent nonidentically distributed exponential random variables. We investigate the dependence structure of these order statistics, and provide a distributional identity that facilitates their simulation and the study of their moment properties. Next, we consider the partial sum Ti — Yl^=i^i ^{j)'> 0 < i < n — 1. We obtain an explicit expression for the cdf of T ,̂ exploiting the memoryless property of the exponential distribution. We do this for the identically distributed case as well, and compare the properties of Ti under the two settings.
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