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Estimation and Prediction for a Progressively First-Failure Censored Inverted Exponentiated Rayleigh Distribution

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Abstract

We discuss inverted exponentiated Rayleigh distribution under progressive first-failure censoring. Maximum likelihood and Bayes estimates of unknown parameters are obtained. An expectation–maximization algorithm is used for computing maximum likelihood estimates. Asymptotic intervals are constructed from the observed Fisher information matrix. Bayes estimates of unknown parameters are obtained under the squared error loss function. We construct highest posterior density intervals based on importance sampling. Different predictors and prediction intervals of censored observations are discussed. A Monte Carlo simulations study is performed to compare different methods. Finally, three real data sets are analyzed for illustration purposes.

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Acknowledgements

The authors are grateful to a reviewer for encouraging comments and constructive suggestions that led to significant improvement in presentation and content of the manuscript. They also thank the Editor for helpful comments. Yogesh Mani Tripathi gratefully acknowledges the partial financial support for this research work under a Grant EMR/2016/001401 Science and Engineering Research Board, India.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Patna, Bihta, 801106, India

    Raj Kamal Maurya & Yogesh Mani Tripathi

  2. Department of Statistics, Patna University, Patna, 800005, India

    Manoj Kumar Rastogi

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  1. Raj Kamal Maurya
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  2. Yogesh Mani Tripathi
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  3. Manoj Kumar Rastogi
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Correspondence to Yogesh Mani Tripathi.

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Maurya, R.K., Tripathi, Y.M. & Rastogi, M.K. Estimation and Prediction for a Progressively First-Failure Censored Inverted Exponentiated Rayleigh Distribution. J Stat Theory Pract 13, 39 (2019). https://doi.org/10.1007/s42519-019-0038-7

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  • DOI: https://doi.org/10.1007/s42519-019-0038-7

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