Reinventing Pareto: Fits for All Losses, Small and Large

Fitting loss distributions in insurance is sometimes a dilemma: either you get a good fit for the small/medium losses or for the very large losses. To be able to get both at the same time, this paper studies generalizations and extensions of the Pareto distribution. This leads not only to a classification of potentially suitable, piecewise defined, distribution functions, but also to new insights into tail behavior and exposure rating.