Download PDF - On the Bayes estimators of the parameters of inflated modified power series distributionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On the Bayes estimators of the parameters of inflated modified power series distributions

Authors 1, 2

Affiliations

  1. Department of Mathematics, Technical University of Lublin, Nadbystrzycka 38 A, 20-618 Lublin
  2. 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

ENG
posterior distributions, posterior moments, Bayes estimator, inflated distribution, generalized Pareto distribution, generalized Poisson distribution, generalized negative binomial distribution, lost games distribution

Bibliography

  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.
Discussiones Mathematicae Probability and Statistics
2000/20/2
Export to PBN, Opens in new tab
Pages:
189-209
Main language of publication
English
Received
1999-06-10
Accepted
2000-01-15
Published
2000

DOI: 10.7151/dmps.1011

Exact and natural sciences