In this paper, we introduce a multiple-inflated Poisson distribution that can handle count data with multiple inflated values. We explore a Bayes predictive distribution for future observation under Kullback Leibler loss function and a class of shrinkage priors, along with plug-in type pmf estimators. To illustrate how well the proposed pmf estimators perform, we provide both a simulated study and a real example analyzing a dataset of National Hockey League (NHL) shootout losses in 2017/18.
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