Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics
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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=∑ j=i+1 n 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.
Keywords and phrasesMarkov property equal in distribution simulation mixtures selection differential
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