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Order Statistics from the Power Lindley Distribution and Associated Inference with Application

Author

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  • Devendra Kumar

    (Central University of Haryana)

  • Anju Goyal

    (Panjab University)

Abstract

Power Lindley distribution has been proposed recently by Ghitany et al. (Comput Stat Data Anal 64:20–33, 2013) as a simple and useful reliability model for analysing lifetime data. This model provides more flexibility than the Lindley distribution in terms of the shape of the density and hazard rate functions as well as its skewness and kurtosis. For this distribution, exact explicit expressions for single moments, product moments, marginal moment generating functions and joint moment generating functions of each of these order statistics are derived. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. In addition, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aodasc:v:6:y:2019:i:1:d:10.1007_s40745-019-00193-9
    DOI: 10.1007/s40745-019-00193-9
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. 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.
    3. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    4. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    5. Mahmoud, M. A. W. & Sultan, K. S. & Amer, S. M., 2003. "Order statistics from inverse weibull distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 149-163, February.
    6. Hassan Bakouch, 2013. "R for statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(4), pages 924-924.
    7. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    8. Mohamed Abdel Wahab Mahmoud & Khalaf Salman Sultan & Safaa Mousa Amer, 2003. "Order statistics from inverse Weibull distribution and characterizations," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 389-401.
    9. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    10. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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    Cited by:

    1. 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.
    2. 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.
    3. Nayabuddin & M. A. Khan, 2022. "A Note on Exact Moments of Order Statistics from Exponentiated Burr XII Distribution," Annals of Data Science, Springer, vol. 9(6), pages 1339-1346, December.
    4. Malik Mansoor Rashid & Kumar Devendra, 2019. "Generalized Pareto Distribution Based On Generalized Order Statistics And Associated Inference," Statistics in Transition New Series, Statistics Poland, vol. 20(3), pages 57-79, September.
    5. repec:exl:29stat:v:20:y:2019:i:3:p:57-80 is not listed on IDEAS
    6. 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.

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