A new discrete distribution with applications to radiation, smoking, and health data

Abstract

In this study, a flexible discrete distribution is introduced by compounding Epanechnikov-exponential and Poisson distributions. Many mathematical features of the distribution are obtained. Several point estimators of the unknown parameter are proposed. The Monte Carlo simulation study is carried out to compare these estimators. Three methods are proposed to construct the approximate confidence intervals for the distribution parameter. A novel zero-inflated regression model is given based on the proposed discrete distribution as an alternative to zero-inflated geometric and zero-inflated Poisson models. The usability of the distribution and the count regression model is demonstrated by some practical data analyses, such as the number of dicentric chromosomes observed after exposure to radiation at doses of 0.600, survey data on health, and smoking habits.