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

94 Actuarial Modelling of Claim Counts
Number of policyholders
30000
20000
10000
0
16507
1361
18–22 23–30
Age
0.32 0.308
27482
0.30
0.28
0.26
0.24
Annual claim frequency
0.22 0.208
0.20
0.18
0.163
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
>30
0.00
18–22 23–30 >30
Age
Figure 2.11 Composition of Portfolio B with respect to Age (left panel) and observed annual claim
frequencies according to Age (right panel).
Figure 2.15 shows that the colour of the car has nearly no influence on the number of
claims. We can notice that 10.1 % of the cars are red.
2.9.3 Poisson Regression with Serial Independence
In this subsection, we assume that the N it s are independent for the different values of
i and t. With the help of the SAS R /STAT procedure GENMOD, we have obtained the
results displayed in Table 2.8 for the model with the 5 explanatory variables presented in
Subsection 2.9.2. The results obtained from a Type 3 analysis are as follows:
Source DF Chi-square Pr>Chi-sq
Gender 1 485 00276
Age 2 17356