IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
A motor insurer fits a Poisson GLM with log link to claim counts, using log(exposure in policy-years) as an offset. The fitted linear predictor for a policy with 0.5 years of exposure is 0.4 (excluding the offset). What is the expected number of claims, to 3 decimal places?
The expected claim count is 0.746. With a log link and log-exposure offset, the mean equals exposure times the exponential of the linear predictor, so 0.5 multiplied by e to the power 0.4 gives about 0.746 claims.
- A0.746Correct
- B1.492
- C0.200
- D0.400
- 0.923
Explanation
With a log link and offset, mu = exposure x exp(linear predictor) = 0.5 x exp(0.4) = 0.5 x 1.4918 = 0.746. Option 1.492 ignores the exposure. Option 0.200 multiplies 0.4 by 0.5 instead of using the exponential.
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