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A note on order statistics in the mixed Erlang case

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  • Landriault, David
  • Moutanabbir, Khouzeima
  • Willmot, Gordon E.

Abstract

The order statistics of an independent sample of mixed Erlang random variables are shown to also be of mixed Erlang form. The mixing weights involve easily evaluated sums of multinomial type terms. A life contingency application is also considered.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:13-18
    DOI: 10.1016/j.spl.2015.06.006
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    References listed on IDEAS

    as
    1. Gordon Willmot & Jae-Kyung Woo, 2007. "On the Class of Erlang Mixtures with Risk Theoretic Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 99-115.
    2. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107044074, October.
    3. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    4. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Solutions Manual for Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107620261, February.
    5. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 73-92.
    6. 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.
    7. Yousry Abdelkader, 2004. "Computing the moments of order statistics from nonidentically distributed Erlang variables," Statistical Papers, Springer, vol. 45(4), pages 563-570, October.
    8. 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.
    9. 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.
    10. Willmot, Gordon E. & Woo, Jae-Kyung, 2015. "On Some Properties Of A Class Of Multivariate Erlang Mixtures With Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 151-173, January.
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    Cited by:

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