On Predictive Distribution of K-Inflated Poisson Models with and Without Additional Information

This paper addresses different approaches in finding the Bayesian predictive distribution of a random variable from a Poisson model that can handle count data with an inflated value of K ∈ N, known as the KIP model. We explore how we can use other source of additional information to find such an estimator. More specifically, we find a Bayesian estimator of future density of random variable Y1 , based on observable X1 from the K1 IP(p1 , λ1 ) model, with and without assuming that there exists another random variable X2 , from the K2 IP(p2 , λ2 ) model, independent of X1 , provided λ1 ≥ λ2 , and compare their performance using simulation method.