Premium
Bayesian Estimation in a Generalized Negative Binomial Distribution
Author(s) -
Islam M. N.,
Consul P. C.
Publication year - 1986
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710280302
Subject(s) - mathematics , statistics , negative binomial distribution , bayes' theorem , beta binomial distribution , beta distribution , bayes estimator , estimator , prior probability , binomial distribution , distribution (mathematics) , beta negative binomial distribution , combinatorics , bayesian probability , poisson distribution , mathematical analysis
A generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m , β, θ)= θ x (1 ‐ θ) m +β x—x for x =0, 1, …, and zero otherwise, where m >0, 0<θ<1 and β=0 or 1≦β<θ −1 . The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b) , to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n −1 for different values of k. .