Discussiones Mathematicae Probability and Statistics 20(2) (2000) 189-209

ON THE BAYES ESTIMATORS OF THE PARAMETERS OF INFLATED MODIFIED POWER SERIES DISTRIBUTIONS

Małgorzata Murat

Department of Mathematics, Technical University of Lublin
Nadbystrzycka 38 A, 20-618 Lublin

Dominik Szynal

Institute of Mathematics, University of Maria Curie-Skłodowska
Marii Curie-Skłodowskiej 1, 20-031 Lublin

Abstract

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 and phrases: posterior distributions; posterior moments; Bayes estimator; inflated distribution; generalized Pareto distribution; generalized Poisson distribution; generalized negative binomial distribution; lost games distribution.

1999 Mathematics Subject Classiffication: 62E10, 60E99.

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Received 10 June 1999
Revised 15 January 2000