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

• Autorzy: Małgorzata Murat , Dominik Szynal
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 62E10: Characterization and structure theory
• 60E99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 189-209

Daty

wydano

2000

otrzymano

1999-06-10

poprawiono

2000-01-15

Twórcy

autor

Małgorzata Murat

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

autor

Dominik Szynal

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmps.1011