Bayesian inference and life testing plans for generalized exponential distribution |
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Authors: | Debasis Kundu and Biswabrata Pradhan |
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Institution: | (1) Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India;(2) Statistical Quality Control & Operations Research Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700108, India |
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Abstract: | Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian
inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that
the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be
obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the
approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and
also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different
sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure
is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained
very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis
has been performed for illustrative purposes.
This work was partially supported by a grant from the Department of Science and Technology, Government of India |
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Keywords: | shape parameter scale parameter Markov Chain Monte Carlo importance Sampling fisher information matrix |
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