Multiple Arbitrarily Inflated Negative Binomial Regression Model and its Application

Abstract This paper presents a new modification of the negative binomial distribution that generalizes both the negative binomial and zero-inflated negative binomial distributions. A novel distribution allows for an arbitrary number of inflation points at arbitrary locations. We discuss some distributional properties for the proposed distribution. We derive several methods to obtain estimates of the unknown parameters. Using the modified distribution we propose a new count regression model. Monte Carlo simulation studies are performed to evaluate the performance of the parameter estimators for both the new distribution and the count regression model. Finally, a real data set is analyzed to determine the superiority of the proposed model.