Tweedie regression models and its geometric sums for (semi-)continuous data

Tweedie regression models (TRMs) are flexible tools to deal with non-negative right-skewed data and can handle semi-continuous data, that is, continuous data with probability mass at zero. The geometric sums of Tweedie random variables lead to the geometric Tweedie distributions. Their corresponding regression models (GTRMs) provide not only additional flexibility to deal with continuous, semi-continuous, heavily right-skewed data but also a possibility of under-variation than TRMs. Estimation and inference based on the likelihood approach for TRMs and GTRMs are challenging owing to the presence of an infinity sum and an intractable integral in the probability function along with non-trivial restrictions on the Tweedie power parameter space. Thus, methods based on quasi-likelihood have been proposed and successfully applied for estimation and inference in these classes of regression models. In this paper, our central focus is upon characterizing as well as comparing TRMs and GTRMs taking into consideration their variation and zero-mass indices. Besides, we attempt to illustrate their application through some data analyses. Furthermore, we discuss the challenges for the computational implementation of such probability distributions and corresponding regression models referring to some available implementations in R. This article is categorized under: Statistical Models > Fitting Models Statistical Models > Generalized Linear Models Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms