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Bayesian Estimation for 3-Component Mixture of Generalized Exponential Distribution

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Abstract

This paper presents the Bayesian analysis of 3-component mixture of generalized exponential distribution. The Bayesian analysis and maximum likelihood estimation of five parameters have been performed by assuming type-I right censored data. Monte Carlo simulation has been adopted for the comparison of Bayes estimates, posterior risks, maximum likelihood estimates and maximum likelihood risks. Furthermore, the study assesses the performance of Bayes and maximum likelihood estimates by using different sample sizes, proportion of mixture components, censoring rates and loss functions. The Bayes estimates are examined by using non-informative Jeffreys and uniform prior under square error loss function, precautionary loss function and DeGroot loss function. The maximum likelihood risks are obtained by using the Fisher information matrix.

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Acknowledgements

The authors would like to thank the Editor in Chief and referees for valuable comments which greatly improved the paper.

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Authors and Affiliations

  1. Department of Basic Sciences, Riphah International University Islamabad, Islamabad, 44000, Pakistan

    Syed Mohsin Ali Kazmi & Muhammad Aslam

Authors
  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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Appendix

Appendix

See Tables 15, 16, 17, 18, 19 and 20.

Table 15 MLE and Bayes estimates using uniform prior under SELF, PLF and DLF with \(\lambda_{1} = 0.25,\lambda_{2} = 0.50, \lambda_{3} = 0.75\), \(p_{1} = 0.20, p_{2} = 0.65\) and \(T = 0.3 ,0.7\)
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Table 16 MLE and Bayes estimates using Jeffreys prior under SELF, PLF and DLF with \(\lambda_{1} = 0.25,\lambda_{2} = 0.50, \lambda_{3} = 0.75\), \(p_{1} = 0.20, p_{2} = 0.65\) and \(T = 0.3 ,0.7\)
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Table 17 MLE and Bayes estimates using uniform prior under SELF, PLF and DLF with \(\lambda_{1} = 0.75,\lambda_{2} = 0.50, \lambda_{3} = 0.25\), \(p_{1} = 0.65, p_{2} = 0.20\) and \(T = 0.3 ,0.7\)
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Table 18 MLE and Bayes estimates using Jeffreys prior under SELF, PLF and DLF with \(\lambda_{1} = 0.75,\lambda_{2} = 0.50, \lambda_{3} = 0.25\), \(p_{1} = 0.65, p_{2} = 0.20\) and \(T = 0.3 ,0.7\)
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Table 19 MLE and Bayes estimates using uniform prior under SELF, PLF and DLF with \(\lambda_{1} = 0.50,\;\lambda_{2} = 0.50, \;\lambda_{3} = 0.50\), \(p_{1} = 0.40, p_{2} = 0.40\) and \(T = 0.3 ,0.7\)
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Table 20 MLE and Bayes estimates using Jeffreys prior under SELF, PLF and DLF with \(\lambda_{1} = 0.50,\;\lambda_{2} = 0.50,\; \lambda_{3} = 0.50\), \(p_{1} = 0.40, p_{2} = 0.40\) and \(T = 0.3 ,0.7\)
Full size table

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Kazmi, S.M.A., Aslam, M. Bayesian Estimation for 3-Component Mixture of Generalized Exponential Distribution. Iran J Sci Technol Trans Sci 43, 1761–1788 (2019). https://doi.org/10.1007/s40995-018-0625-6

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  • DOI: https://doi.org/10.1007/s40995-018-0625-6

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