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Computing the moments of order statistics from nonidentical random variables

Author

Listed:
  • H. M. Barakat

    (Zagazig University)

  • Y. H. Abdelkader

    (Alexandria University)

Abstract

. In this paper, we establish new representations, identities and recurrence relations of order statistics (o.s.) arising from general independent nonidentically distributed random variables (r.v.’s). These recurrence relations will enable one to compute all moments of all o.s. in a simple manner. Applications for some known distributions are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:13:y:2004:i:1:d:10.1007_s10260-003-0068-9
    DOI: 10.1007/s10260-003-0068-9
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    Citations

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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. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    3. Jiang, Jun & Shang, Pengjian & Zhang, Zuoquan & Li, Xuemei, 2018. "The multi-scale high-order statistical moments of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 474-488.
    4. Rasool Roozegar & G. G. Hamedani & Leila Amiri & Fatemeh Esfandiyari, 2020. "A New Family of Lifetime Distributions: Theory, Application and Characterizations," Annals of Data Science, Springer, vol. 7(1), pages 109-138, March.
    5. H. M. Barakat & Haidy A. Newer, 2022. "Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size," Statistical Papers, Springer, vol. 63(6), pages 1801-1827, December.
    6. 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.
    7. Lemonte, Artur J. & Cordeiro, Gauss M., 2011. "The exponentiated generalized inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 506-517, April.
    8. Ruijie Guan & Xu Zhao & Weihu Cheng & Yaohua Rong, 2021. "A New Generalized t Distribution Based on a Distribution Construction Method," Mathematics, MDPI, vol. 9(19), pages 1-36, September.
    9. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
    10. Gauss Cordeiro & Artur Lemonte, 2013. "On the Marshall–Olkin extended Weibull distribution," Statistical Papers, Springer, vol. 54(2), pages 333-353, May.
    11. 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.
    12. 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.
    13. Saralees Nadarajah, 2006. "Explicit expressions for moments of beta order statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 377-384.
    14. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    15. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.

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