A Primer on the Exponential Family of Distributions

Generalized Linear Model (GLM) theory represents a significant advance beyond linear regression theory, specifically in expanding the choice of probability distributions from the Normal to the Natural Exponential Family. This Primer is intended for GLM users seeking a handy reference on the model’s distributional assumptions. The Exponential Family of Distributions is introduced, with an emphasis on variance structures that may be suitable for aggregate loss models in property casualty insurance.