BAYESIAN INFERENCE ON A MIXTURE OF GEOMETRIC AND DEGENERATE DISTRIBUTION:A SPECIAL CASE OF ZERO INFLATED GEOMETRIC DISTRIBUTION AND POSTERIOR ODDS RATIO

Volume : V, Issue : VIII, August - 2016

Maitreya N. Acharya

Here, we have developed a change point model by considering the mixture of two distributions. Let us consider

that a random sequence of X1, X2, X3,. . . ,Xm was observed from the Zero Inflated Geometric Distribution with

proportion p_1 and θ_1. Later it was found that there was a change in the system at some unknown point of time �m� (m

in the sequence after Xm with proportion p_2 and θ_2. Then we have obtained the Posterior Odds Ratio (POR) of the change point

�m� under beta priors and also under non–informative prior. In the next section, we have obtained posterior densities of �m� for p_1 and

p_2 known using beta prior under H_1 and H_0 respectively. Then, we have obtained the marginal posterior densities of �m� for p_1 and

p_2 known using non–informative prior of θ_1and θ_2 under H_1 and H_0 respectively. Later, numerical study is done on the generated

observations. In the last section, we have studied the sensitivity of Posterior Odds Ratio with respect to change in prior of the parameters