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On Some Estimation Methods for the Inverse Pareto Distribution

Author

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  • Indrajeet Kumar

    (Central University of Haryana)

  • Shishir Kumar Jha

    (University of Delhi)

  • Kapil Kumar

    (Central University of Haryana)

Abstract

There are many real-life situations, where data require probability distribution function which have decreasing or upside down bathtub (UBT) shaped failure rate function. The inverse Pareto distribution consists both decreasing and UBT shaped failure rate functions. Here, we address the different estimation methods of the parameter and reliability characteristics of the inverse Pareto distribution from both classical and Bayesian approaches. We consider several classical estimation procedures to estimate the unknown parameter of inverse Pareto distribution, such as maximum likelihood, method of percentile, maximum product spacing, the least squares, weighted least squares, Anderson–Darling, right-tailed Anderson–Darling and Cramér–Von-Mises. Also, we consider Bayesian estimation using squared error loss function based on conjugate and Jefferys’ priors. An extensive Monte Carlo simulation experiment is carried out to compare the performance of different estimation methods. For illustrative purposes, we have considered two real data sets.

Suggested Citation

  • Indrajeet Kumar & Shishir Kumar Jha & Kapil Kumar, 2023. "On Some Estimation Methods for the Inverse Pareto Distribution," Annals of Data Science, Springer, vol. 10(4), pages 1035-1068, August.
    • Handle: RePEc:spr:aodasc:v:10:y:2023:i:4:d:10.1007_s40745-021-00356-7
    DOI: 10.1007/s40745-021-00356-7
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    References listed on IDEAS

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    1. Md. Mahabubur Rahman & Bander Al-Zahrani & Muhammad Qaiser Shahbaz, 2020. "Cubic Transmuted Pareto Distribution," Annals of Data Science, Springer, vol. 7(1), pages 91-108, March.
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    3. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    4. Muhammad Aslam & Rahila Yousaf & Sajid Ali, 2020. "Bayesian Estimation of Transmuted Pareto Distribution for Complete and Censored Data," Annals of Data Science, Springer, vol. 7(4), pages 663-695, December.
    5. Kapil Kumar, 2018. "Classical and Bayesian estimation in log-logistic distribution under random censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(2), pages 440-451, April.
    6. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
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