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

Risk Classification 95
Number of policyholders
30000
20000
10000
0
29024
0.19
0.188
0.18
0.177
0.17
0.16
0.15
0.14
0.13
0.12
16326
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
Female Male
0.00
Female Male
Gender
Annual claim frequency
Gender
Figure 2.12 Composition of Portfolio B with respect to Gender (left panel) and observed annual
claim frequencies according to Gender (right panel).
The variable Colour is not relevant, as the p-value is 56.98 % according to the Type 3
analysis. The variable Power could then also be removed (p-value of 11.21 % after having
removed the variable Colour from the regression model) but since this variable is common
in the tariff of insurers, we will try an interaction between the variables Age and Power.
The interaction between Age and Power is illustrated in Figure 2.16 (where ‘LP’ stands
for large power, that is, over 110 kW, ‘MP’ stands for medium power, that is, between 66
and 110 kW, and ‘SP’ for small power, that is, less than 66 kW). The results are given in
Table 2.9. The Type 3 analysis is as follows:
Source DF Chi-square Pr>Chi-sq
Gender 1 486 0.0275
Age ∗ Power 8 18001