BAYESIAN INFERENCE ON MIXTURE OF GEOMETRIC WITH DEGENERATE DISTRIBUTION: ZERO INFLATED GEOMETRIC DISTRIBUTION

Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated Geometric distribution is a mixture of a Geometric distribution and a degenerate distribution at zero, with a mixing probability p for the degenerate distribution. This distribution is useful for modeling count data that may have extra zeros. A sequence of independent count data X1,....... Xm, Xm+1,......, Xnwere observed from A zero-inflated Geometric extra zeros. A sequence of independent count data X1,......, Xm, Xm+1,......, Xn were observed from A zero-inflated Geometric distribution with probability mass function f xi p1 , θ1 ,but later it was found that there was a change in the system at some point m and it is reflected in the sequence after Xm by change in probability mass function f ∗ xi p2 , θ2 . The Bayes estimators of m , θ1 , p1,θ2 ,p2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.