IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
A gamma GLM for claim severity uses the log link with η = 6.5 + 0.3x1 − 0.2x2. Policy A has (x1,x2)=(2,1) and policy B has (x1,x2)=(0,3). What is the ratio of fitted mean of A to that of B?
The ratio is e^1.0, about 2.72. The linear predictors are 6.9 for A and 5.9 for B, and under the log link the ratio of means is the exponential of their difference.
- Ae^0.4 ≈ 1.49
- Be^1.2 ≈ 3.32
- Ce^0.6 ≈ 1.82
- De^1.0 ≈ 2.72Correct
- e^0.2 ≈ 1.22
Explanation
ηA = 6.5+0.6−0.2 = 6.9. ηB = 6.5−0.6 = 5.9. Difference = 1.0, so ratio = e^1.0 ≈ 2.72. The intercept cancels in the ratio.
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