The Negative Binomial-Bilal Distribution: Regression Model and Applications to Health Care Data

In health care research, overdispersion often arises in count data. The Poisson distribution is a traditional distribution for modeling count data. However, it cannot handle overdispersed count data. This article introduces a new count distribution for overdispersed data. Statistical properties and a multivariate version of the proposed distribution are derived. Two parameter estimation methods are discussed by the maximum likelihood method and Bayesian approach. A simulation study is conducted to assess the performance of the estimators. A regression model based on the proposed distribution is constructed. Finally, two health care applications are analyzed to show the potential of the proposed distribution and its associated regression model.