Discussiones Mathematicae Probability and Statistics 20(2) (2000) 189-209
Małgorzata Murat Department of Mathematics, Technical University of
Lublin |
Dominik Szynal Institute of Mathematics, University of Maria
Curie-Skłodowska |
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.
[1] | M. Ahsanullah, Recurrence relations for single and product moments of record values from generalized Pareto distribution, Commun. Statist.-Theory Meth. 23 (10) (1994), 2841-2852. |
[2] | H. Cramér, Mathematical Methods of Statistics, 1945. |
[3] | P.L. Gupta, R.C. Gupta and R.C. Tripathi, Inflated modified power series distribution, Commun. Statist.-Theory Meth. 24 (9) (1995), 2355-2374. |
[4] | K.G. Janardan, Moments of certain series distributions and their applications, J. Appl. Math. 44 (1984), 854-868. |
[5] | A.W. Kemp and C.D. Kemp, On a distribution associated with certain stochastic processes, J. Roy. Statist. Soc. Ser. B, 30 (1968), 160-163. |
[6] | M. Murat and D. Szynal, Non-zero inflated modified power series distributions, Commun. Statist.-Theory Meth. 27 (12) (1998), 3047-3064. |
[7] | K.N. Pandey, Generalized inflated Poisson distribution, J. Scienc. Res. Banares Hindu Univ., XV (2) (1964-65), 157-162. |
[8] | J. Pikands, Statistical inference using extreme order statistics, Ann. Statist. 3 (1) (1975), 119-131. |
Received 10 June 1999
Revised 15 January 2000