Estimation, Evaluation, and Selection of Actuarial Models

4 CHAPTER 2. MODEL ESTIMATION
Throughout this Note, four examples will used repeatedly. Because they are simply data sets,
they will be referred to as Data Sets A, B, C and D.
Data Set A This data set is well-known in the casualty actuarial literature. It was first analyzed in
the paper “Some Considerations on Automobile Rating Systems Using Individual Driving Records,”
by L. Dropkin in the 1959 Proceedings of the Casualty Actuarial Society (pages 165—176). He
collected data from 1956—1958 on the number of accidents by one driver in one year. The results
for 94,935 drivers are in the following table.
Number of accidents Number of drivers
0 81,714
1 11,306
2 1,618
3 250
4 40
5ormore 7
Data Set B Thesenumbersareartificial. They represent the amounts paid on workers compensation
medical benefits, but are not related to any particular policy or set of policyholders. These
payments are the full amount of the loss. A random sample of 20 payments was taken.
27 82 115 126 155 161 243 294 340 384
457 680 855 877 974 1,193 1,340 1,884 2,558 15,743
Data Set C These observations are similar to Table 2.18 on Page 127 of Loss Models.
represent payments on 227 claims from a general liability insurance policy.
They
Payment range Number of payments
0—7,500 99
7,500—17,500 42
17,500—32,500 29
32,500—67,500 28
67,500—125,000 17
125,000—300,000 9
over 300,000 3
Data Set D Thesenumbersareartificial. They represent the time at which a five-year term
insurance policy terminates. For some policyholders, termination is by death, for some it is by
surrender (the cancellation of the insurance contract), and for the remainder it is expiration of the
five-year period. Two separate versions are presented. For Data Set D1, there were 30 policies
observed from issue. For each, both the time of death and time of surrender are presented, provided
they were before the expiration of the five-year period. Of course, normally we do not know when
policyholders who surrendered would have died had they not surrendered and we do not know when
policyholders who died would have surrendered had they not died. Note that the final 12 policyholders
survivedbothdeathandsurrendertotheendofthefive-year period.