A novel flexible three-parameter zero-inflated discrete distribution with applications in medical-related fields

In this paper, we offer a novel flexible three-parameter zero-inflated discrete distribution that proves to be ideal for the analysis of over-dispersed count data. The first contribution is to determine some of its key properties, such as mean, variance, and expressions for the main generating functions. We then emphasize inference and data analysis applications. The estimation of the three unknown parameters is carried out by means of the maximum likelihood estimation method. Based on the examination of six real data sets, the proposed distribution highlights its practical relevance and versatility in different scenarios. Furthermore, the applied component is fully transparent to the reader: the R computational codes for the proposed distribution are constructed and included in the appendix.