On the mean-parameterized Bell–Touchard regression model for count data

Abstract

The two-parameter Bell–Touchard distribution corresponds to a quite flexible yet tractable parametric family of discrete distributions, which arises prominently as an empirical model for count data. In this paper, we introduce a novel parametric regression model for count response variables on the basis of the mean-parameterized Bell–Touchard distribution, which allows interpretation of the regression coefficients in terms of the expectation of the count response variable, like the generalized linear model framework. The unknown parameters of the mean-parameterized Bell–Touchard regression model are estimated using the traditional maximum likelihood estimation procedure. We also consider the deviance residuals to assess departures from model assumptions. Empirical applications are provided to illustrate the mean-parameterized Bell–Touchard regression model in practice, and comparisons with some popular existing count regression models are made.