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

Małgorzata Murat; Dominik Szynal

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 2, page 189-209
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Małgorzata Murat, and Dominik Szynal. "On the Bayes estimators of the parameters of inflated modified power series distributions." Discussiones Mathematicae Probability and Statistics 20.2 (2000): 189-209. <http://eudml.org/doc/287733>.

@article{MałgorzataMurat2000,
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.},
author = {Małgorzata Murat, Dominik Szynal},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {posterior distributions; posterior moments; Bayes estimator; inflated distribution; generalized Pareto distribution; generalized Poisson distribution; generalized negative binomial distribution; lost games distribution; lost games distributions},
language = {eng},
number = {2},
pages = {189-209},
title = {On the Bayes estimators of the parameters of inflated modified power series distributions},
url = {http://eudml.org/doc/287733},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Małgorzata Murat
AU - Dominik Szynal
TI - On the Bayes estimators of the parameters of inflated modified power series distributions
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 2
SP - 189
EP - 209
AB - 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.
LA - eng
KW - posterior distributions; posterior moments; Bayes estimator; inflated distribution; generalized Pareto distribution; generalized Poisson distribution; generalized negative binomial distribution; lost games distribution; lost games distributions
UR - http://eudml.org/doc/287733
ER -

References

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  1. [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. Zbl0850.62118
  2. [2] H. Cramér, Mathematical Methods of Statistics, 1945. 
  3. [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. [4] K.G. Janardan, Moments of certain series distributions and their applications, J. Appl. Math. 44 (1984), 854-868. Zbl0556.62011
  5. [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. [6] M. Murat and D. Szynal, Non-zero inflated modified power series distributions, Commun. Statist.-Theory Meth. 27 (12) (1998), 3047-3064. Zbl0924.62017
  7. [7] K.N. Pandey, Generalized inflated Poisson distribution, J. Scienc. Res. Banares Hindu Univ., XV (2) (1964-65), 157-162. 
  8. [8] J. Pikands, Statistical inference using extreme order statistics, Ann. Statist. 3 (1) (1975), 119-131. Zbl0312.62038

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