The compound Poisson distribution with gamma claim
sizes is a very common model for premium
estimation in Property and Casualty
insurance. Under this distributional assumption,
generalised linear models (GLMs) are used to
estimate the mean claim frequency and severity,
then these estimators are simply multiplied to
estimate the mean aggregate loss.
 
The Tweedie distribution allows to parametrise the
compound Poisson-gamma (CPG) distribution as a
member of the exponential dispersion family and
then fit a GLM with a CPG distribution for the
response. Thus, with the Tweedie distribution it
is possible to estimate the mean aggregate loss
using GLMs directly, without the need to
previously estimate the mean frequency and
severity separately.

The purpose of this educational note is to explore
the differences between these two estimation
methods, contrasting the advantages and
disadvantages of each.