Loss Models: From Data to Decisions, 4th Edition

9.2 Model choices

In many cases of fitting frequency or severity distributions to data, several distributions may be good candidates for models. However, some distributions may be preferable for a variety of practical reasons.

In general, it is useful for the severity distribution to be a scale distribution (see Definition 4.2) because the choice of currency (e.g., U.S. dollars or British pounds) should not affect the result. Also, scale families are easy to adjust for inflationary effects over time (this is, in effect, a change in currency; e.g., 1994 U.S. dollars to 1995 U.S. dollars). When forecasting the costs for a future year, the anticipated rate of inflation can be factored in easily by adjusting the parameters.

A similar consideration applies to frequency distributions. As an insurance company’s portfolio of contracts grows, the number of claims can be expected to grow, all other things being equal. Models that have probability generating functions of the form

(9.2)

for some parameter α have the expected number of claims proportional to α. Increasing the volume of business by 100r% results in expected claims being proportional to α* = (1 + r)α. This approach is discussed in Section 7.4. Because r is any value satisfying r > −1, the distributions satisfying (9.2) should allow a to take on any positive values. Such distributions can be shown to be infinitely divisible (see ...