Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

232 Actuarial Modelling of Claim Counts
so that the moment generating function of C i is
n∏
j=1
( ) ( t
M = 1 − t ) − ′
i
i
n i i
′
where ′ i = n i. Hence, the arithmetic average of the C ik s conforms to the am i n i i
distribution. This situation is accounted for in GENMOD by specifying an appropriate
weight n i .
Example 5.1 (Gamma Regression for the Moderate Claim Costs in Portfolio C) The
Gamma regression performed on the claim costs recorded in Portfolio C leads to the results
in Table 5.3 where the following variables have been eliminated: Fuel (p-value of 9476 %),
Gender (p-value of 8889 %), Use (p-value of 2748 %) and Power (p-value of 928 %).
Moreover, for Agev, levels 6–10 and > 10 have been grouped together in a class > 5. For
the variable Ageph, levels 31–60 and > 60 have been grouped in a class > 30. The resulting
log-likelihood is equal to −147 62910. Type 3 analysis is presented in the following table:
Source DF Chi-square Pr>Chi-sq
Ageph 2 6592