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On Some Estimation Methods for the Inverse Pareto Distribution

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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.

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Acknowledgements

The authors are grateful to the Editor-in-Chief and anonymous referees for their valuable comments and suggestions, which lead to an improved version of this article.

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The authors received no specific funding for this study.

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Authors and Affiliations

  1. Department of Statistics, Central University of Haryana, Mahendergarh, 123031, India

    Indrajeet Kumar & Kapil Kumar

  2. Department of Statistics, Ramjas College, University of Delhi, New Delhi, Delhi, 110007, India

    Shishir Kumar Jha

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  1. Indrajeet Kumar
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  2. Shishir Kumar Jha
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  3. Kapil Kumar
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Correspondence to Kapil Kumar.

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Writing and original draft by Indrajeet Kumar; Writing, review and editing by Kapil Kumar and Shishir Kumar Jha.

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Kumar, I., Jha, S.K. & Kumar, K. On Some Estimation Methods for the Inverse Pareto Distribution. Ann. Data. Sci. 10, 1035–1068 (2023). https://doi.org/10.1007/s40745-021-00356-7

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  • DOI: https://doi.org/10.1007/s40745-021-00356-7

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