Order statistics from independent exponential random variables and the sum of the top order statistics

Let X-(1) < (...) < X-(n) 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 T-i = Sigma(n)(j=i+1) X-(j), 0 <= i <= n-1. We obtain an explicit expression for the cdf of T-i, exploiting the memoryless property of the exponential distribution. We do this for the identically distributed case as well, and compare the properties of T-i under the two settings.