Distributions for Actuaries

This monograph contains a brief exposition of the standard probability distributions—and their fundamental applications—commonly encountered by property/casualty actuaries. Specifically, it includes the basic distributional topics that I had occasion to use during the 25 years I provided actuarial support to the excess and surplus lines underwriting departments at the St. Paul Companies (now Travelers). The emphasis is on a clear, informal presentation of the basic concepts, and there has been no attempt to provide an exhaustive (and possibly, exhausting) compendium of every possible topic and technique. Moreover, the focus is clearly on the use of parametric distributions fitted to empirical claim data to solve standard actuarial problems—creation of increased limit factors, pricing of deductibles, evaluating the effect of aggregate limits, and so on.

Keywords: Probability Distributions; Claim Counts; Aggregate Claims; Risk Load; Variability