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

88 Actuarial Modelling of Claim Counts
2.7.2 Numerical Illustration
The GENMOD procedure of SAS R does not support the Poisson-LogNormal model. We
have computed the regression coefficients with the aid of the NLMIXED procedure of SAS R .
The results are given in Table 2.6 and the estimation of 2 is equal to 07064 which leads to
̂ = ̂V i = 1027
for the variance of the random effect. We observe that this value is greater than those obtained
in the Poisson-Inverse Gaussian model and in the Negative Binomial model. The resulting
regression coefficients are similar to those obtained previously. The log-likelihood is equal
to −54481 and is intermediate between the log-likelihoods of the Negative Binomial model
and of the Poisson-Inverse Gaussian model (which is the maximum). The variance-covariance
matrix of the estimated regression coefficients and ̂ 2 is
̂̂
=
⎛
⎞
0002438 −0001546 −0001474 −0001047 −0001036 −0001543 0000075
−0001546 0003270 0001707 −0000082 −0000287 0000831 0000064
−0001474 0001707 0006104 −0000224 −0000548 0001088 0000354
−0001047 −0000082 −0000224 0002875 0000218 −0000022 −0000050
⎜
⎝ −0001036 −0000287 −0000548 0000218 0003056 0000687 0000188 ⎟
⎠
−0001543 0000831 0001088 −0000022 0000687 0006825 0000058
0000075 0000064 0000354 −0000050 0000188 0000058 0008056
The Type 3 analysis for the final model gives
Source DF Chi-square Pr>Chi-sq
Gender ∗ Age 2 660