The zero-inflated Conway–Maxwell–Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

In this paper we propose the zero-inflated COM-Poisson distribution. We develop a Bayesian analysis for our model via on Markov chain Monte Carlo methods. We discuss regression modeling and model selection, as well as, develop case deletion influence diagnostics for the joint posterior distribution based on the ψψ-divergence, which has several divergence measures as particular cases, such as the Kullback–Leibler (K–L), JJ-distance, L1L1 norm and χ2χ2-square divergence measures. The performance of our approach is illustrated in an artificial dataset as well as in a real dataset on an apple cultivar experiment.