Abstract
In this work the regression model to k-Modified family distributions is proposed. It is understood as modification, the inclusion of a parameter in the probability mass function of the traditional discrete distributions, which is able to model inflation or deflation of the observation k in the dataset. The modification in relation to the original distribution becomes necessary when, in many practical situations, a specific observation k occurrs in the dataset with higher or lower frequency than what is expected by considering a specific discrete distribution. In the context of regression models, discrete distributions with probability mass function that can be written through their means will be considered.