Loss Ratio Distribution - A Model

In this paper are set forth some important mathematical properties of the gamma distribution (Chapter 2) including the very important characteristic of reproductivity and divisibility. In most instances the development of formulas and lemmas is left to the reference texts, or the reader. The gamma distribution is applied directly to loss ratio distributions as a model (Chapter 3) and a single parameter form is asserted. In Chapter 4 the method of fitting actual data is explained and the goodness of the fit is discussed. A relationship among parameters at various premium sizes is also asserted. As a corollary it becomes evident that for actual data, loss ratio distributions for larger premium sizes are not equivalent to loss ratio distributions that might have been obtained by taking random samples from small premium sizes. An attempt is made to account for this phenomenon. Finally, (Chapter 5) the utility of the new model is discussed for: (1) linear retrospective rating (2) Non-linear retrospective rating (3) Competitive "retro" dividend plans.