Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics

  • H. N. Nagaraja
Part of the Statistics for Industry and Technology book series (SIT)


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≥in−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 phrases

Markov property equal in distribution simulation mixtures selection differential 


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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • H. N. Nagaraja
    • 1
  1. 1.The Ohio State UniversityColumbusUSA

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