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A Laplace transform method for order statistics from nonidentical random variables and its application in Phase-type distribution

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  • Abdelkader, Yousry H.

Abstract

In this paper, we derive a method for obtaining the Laplace transform of order statistics (o.s.) arising from general independent nonidentically distributed random variables (r.v.'s). A survey of the most important properties, applications and the o.s. of a Phase-type (PH) distribution are also presented. Two illustrative examples are provided.

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  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1143-1149
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    References listed on IDEAS

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    1. Kamburowski, Jerzy, 1985. "An upper bound on the expected completion time of PERT networks," European Journal of Operational Research, Elsevier, vol. 21(2), pages 206-212, August.
    2. Mary A. Johnson, 1993. "Selecting Parameters of Phase Distributions: Combining Nonlinear Programming, Heuristics, and Erlang Distributions," INFORMS Journal on Computing, INFORMS, vol. 5(1), pages 69-83, February.
    3. 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.
    4. 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.
    5. Yousry Abdelkader, 2010. "Adjustment of the moments of the project completion times when activity times are exponentially distributed," Annals of Operations Research, Springer, vol. 181(1), pages 503-514, December.
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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.

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