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On Estimation of Type-II Progressive Censored Erlang Distribution

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Abstract

Progressive censoring has become popular in recent years. In this paper, Type-II progressive censored Erlang distribution has been used for Bayesian estimation and maximum likelihood estimation. Method of elicitation has also been employed by using prior predictive distributions to compute the values of hyperparameters. Moreover, real-life data and rigorous simulation schemes have been exercised for Bayesian shrinkage estimates, Bayesian estimates, and maximum likelihood estimates along with their associated posterior risks. Furthermore, the results of Bayes estimates are obtained by using a generalized entropy loss function. During this meticulous exercise, it has been observed that by increasing the effective sample size \(n\), risks become decrease and the Bayes estimates turn out to be closer to the true value of the parameters. But at the same time, both Bayes estimates and risks are not affected by changing the sample size \(m\). Additionally, Bayesian shrinkage estimation is more tractable than Bayesian estimation and maximum likelihood estimation especially when prior information about the parameter is known in the form of point guess value.

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(i) Real-life data: See Sect. 9, Tables 2, 3. (ii) Simulation Studies: See Sect. 8, Table 4

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Acknowledgements

Authors wish to thank the referees and chief editor for their valuable comments which led to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Riphah International University Islamabad, Islamabad, Pakistan

    Syed Mohsin Ali Kazmi & Muhammad Aslam

  2. Sustainable Development Policy Institute, Islamabad, Pakistan

    Syed Mohsin Ali Kazmi

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  1. Syed Mohsin Ali Kazmi
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  2. Muhammad Aslam
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Correspondence to Syed Mohsin Ali Kazmi.

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Kazmi, S.M.A., Aslam, M. On Estimation of Type-II Progressive Censored Erlang Distribution. J Indian Soc Probab Stat 23, 565–584 (2022). https://doi.org/10.1007/s41096-022-00140-7

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