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Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application

Author

Listed:
  • Devendra Kumar

    (Central University of Haryana)

  • Neetu Jain

    (University of Delhi)

  • Mazen Nassar

    (King Abdulaziz University
    Zagazig University)

  • Osama Eraki Abo-Kasem

    (Zagazig University)

Abstract

Exponentiated Kumaraswamy-power function (EKPF) distribution has been proposed recently by Bursa and Ozel (Hacet J Math Stat 46:277–292, 2017) as a quite flexible in terms of probability density and hazard rate functions than power function distribution. In this paper, we obtain the explicit expressions for the single, double (product), triple and quadruple moments and moment generating function for single, double, triple and quadruple of order statistics of the EKPF distribution. By using these relations, we have tabulated the means and variances of order statistics from samples of sizes up to 10 for various values of the parameters. We use five frequentist estimation methods to estimate the unknown parameters and a simulation study is used to compare the performance of the different estimators. Finally, we analyse a real data set for illustrative purpose.

Suggested Citation

  • Devendra Kumar & Neetu Jain & Mazen Nassar & Osama Eraki Abo-Kasem, 2021. "Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application," Annals of Data Science, Springer, vol. 8(4), pages 785-811, December.
    • Handle: RePEc:spr:aodasc:v:8:y:2021:i:4:d:10.1007_s40745-019-00233-4
    DOI: 10.1007/s40745-019-00233-4
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    References listed on IDEAS

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    1. Udo Kamps, 1991. "A general recurrence relation for moments of order statistics in a class of probability distributions and characterizations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 215-225, December.
    2. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.
    3. Devendra Kumar & Sanku Dey & Saralees Nadarajah, 2017. "Extended exponential distribution based on order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9166-9184, September.
    4. Devendra Kumar & Anju Goyal, 2019. "Order Statistics from the Power Lindley Distribution and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(1), pages 153-177, March.
    5. Devendra Kumar & Anju Goyal, 2019. "Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(4), pages 707-736, December.
    6. Mansoor Rashid Malik & Devendra Kumar, 2019. "Generalized Pareto Distribution Based On Generalized Order Statistics And Associated Inference," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 57-79, September.
    7. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
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