Generalized exponential distribution: Bayesian estimations |
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Authors: | Debasis Kundu Rameshwar D Gupta |
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Affiliation: | a Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India b Department of Computer Science and Applied Statistics, The University of New Brunswick, Saint John, Canada E2L 4L5 |
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Abstract: | Recently two-parameter generalized exponential distribution has been introduced by the authors. In this paper we consider the Bayes estimators of the unknown parameters under the assumptions of gamma priors on both the shape and scale parameters. The Bayes estimators cannot be obtained in explicit forms. Approximate Bayes estimators are computed using the idea of Lindley. We also propose Gibbs sampling procedure to generate samples from the posterior distributions and in turn computing the Bayes estimators. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes. |
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Keywords: | Bayes estimator Maximum likelihood estimator Gamma distribution Log-concave density function Squared error loss function Posterior density function |
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