Yesterday, I was chating with a young and enthousiastic actuary, who asked a nice (and classical) question: is it the same, or not to use a Tweedie regression, or two regressions (Poisson, and Gamma). For distributions, the two are equivalent, but when we have heterogeneity and explanatory variable, I really think that using all information, and running two regressions is much more interesting. Homogeneous case In the homogenous case, without any explanatory variable, the Tweedie distribution and compound Poisson-gamma distribution are equivalent representation (i.e., … <a …