A new regression model for count data with applications to health care data

Count data regression is one of the widely used techniques for modelling medical data and has applications in various other fields as well. Count data usually exhibits the characteristic of over-dispersion and new models are developed to open up the opportunity to model such kind of data. This paper introduces a new probability model namely two parameter Poisson-Xgamma distribution and its associated count data regression model is also developed. The structural properties of the proposed probability model like moments, skewness, kurtosis and generating functions among others have been derived. The parameter estimation for the proposed model is discussed using two well-known methods. A Monte Carlo simulation is carried out to investigate the finite sample behavior of maximum likelihood estimates for parameters of new regression model. Furthermore, the empirical applications of the proposed probability model and its associated regression model are validated using two health care data sets. Based on some famous statistical criteria, the proposed model demonstrates better fitting results as compared to other existing discrete models.