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

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Book cover Advances in Distribution Theory, Order Statistics, and Inference

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

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=∑ nj=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.

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Author information

Authors and Affiliations

  1. The Ohio State University, Columbus, OH, USA

    H. N. Nagaraja

Authors
  1. H. N. Nagaraja
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

  2. Department of Economics, University of Cantabria, s/n Avenida de los Castros, Santander, 39005, Spain

    José María Sarabia  & Enrique Castillo  & 

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© 2006 Birkhäuser Boston

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Nagaraja, H.N. (2006). Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics. In: Balakrishnan, N., Sarabia, J.M., Castillo, E. (eds) Advances in Distribution Theory, Order Statistics, and Inference. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4487-3_11

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