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A method for obtaining Laplace transforms of order statistics of Erlang random variables

Author

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  • Hlynka, M.
  • Brill, P.H.
  • Horn, W.

Abstract

We present a path-counting method for deriving Laplace transforms of order statistics of independent but not necessarily identically distributed Erlang random variables, based on a probabilistic interpretation of the Laplace transform. The method is applicable also to generalized Erlang variates having different parameters for the exponential stages. The idea is to provide an intuitive understanding of the Laplace transform, based on the Markovian properties of the stages of the Erlang random variable. Thus the derivation technique is applicable to many other Markovian stochastic models. Motivational examples for queues and reliability are mentioned. Computational considerations are discussed.

Suggested Citation

  • Hlynka, M. & Brill, P.H. & Horn, W., 2010. "A method for obtaining Laplace transforms of order statistics of Erlang random variables," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 9-18, January.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:1:p:9-18
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    References listed on IDEAS

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    1. Brill, P. H. & Hlynka, M., 2000. "An exponential queue with competition for service," European Journal of Operational Research, Elsevier, vol. 126(3), pages 587-602, November.
    2. H. M. Barakat & Y. H. Abdelkader, 2004. "Computing the moments of order statistics from nonidentical random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(1), pages 15-26, April.
    3. Yousry Abdelkader, 2004. "Computing the moments of order statistics from nonidentically distributed Erlang variables," Statistical Papers, Springer, vol. 45(4), pages 563-570, October.
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    Cited by:

    1. Landriault, David & Moutanabbir, Khouzeima & Willmot, Gordon E., 2015. "A note on order statistics in the mixed Erlang case," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 13-18.
    2. Abdelkader, Yousry H., 2011. "A Laplace transform method for order statistics from nonidentical random variables and its application in Phase-type distribution," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1143-1149, August.

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