K 1 K 2–Inflated Conway–Maxwell–Poisson Model: Bayesian Predictive Modeling with an Application in Soccer Matches

Abstract The purpose of this paper is two folds. First, to introduce a multiple inflated version of the Conway–Maxwell–Poisson model, that can be used flexibly to model count data when some values have high frequency along with over– or under–dispersion. Also, this model includes Poisson, Conway–Maxwell–Poisson (COMP), zero–inflated Poisson (ZIP), multiple–inflated Poisson, and zero–inflated Conway–Maxwell–Poisson (ZICOMP). Second, to estimate the future distribution from the multiple inflated Conway–Maxwell–Poisson model under the Kullback Leibler difference (loss) function. This model is fitted to the number of penalties scored in the Premier League’s 2019–20 season and its future distribution using Bayes and plug–in methods is estimated.