  A flexible semiparametric class of models is introduced that offers an
alternative to classical regression models for count data as the Poisson and
negative binomial model, as well as to more general models accounting for
excess zeros that are also based on fixed distributional assumptions. The model
allows that the data itself determine the distribution of the response
variable, but, in its basic form, uses a parametric term that specifies the
effect of explanatory variables. In addition, an extended version is
considered, in which the effects of covariates are specified nonparametrically.
The proposed model and traditional models are compared by utilizing several
real data applications.
