Geodesic
On the Bayes estimators of the parameters of inflated modified power series distributions
Discussiones Mathematicae. Probability and Statistics, Tome 20 (2000) no. 2, pp. 189-209.

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In this paper, we study the class of inflated modified power series distributions (IMPSD) where inflation occurs at any of support points. This class includes among others the generalized Poisson,the generalized negative binomial and the lost games distributions. We derive the Bayes estimators of parameters for these distributions when a parameter of inflation is known. First, we take as the prior distribution the uniform, Beta and Gamma distribution. In the second part of this paper, the prior distribution is the generalized Pareto distribution.
Keywords: posterior distributions, posterior moments, Bayes estimator, inflated distribution, generalized Pareto distribution, generalized Poisson distribution, generalized negative binomial distribution, lost games distribution 
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Murat, Małgorzata; Szynal, Dominik. On the Bayes estimators of the parameters of inflated modified power series distributions. Discussiones Mathematicae. Probability and Statistics, Tome 20 (2000) no. 2, pp. 189-209. http://geodesic.mathdoc.fr/item/DMPS_2000_20_2_a2/

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