IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
A Poisson GLM with log link models claim counts with linear predictor η = β0 + β1·(age band B) + log(exposure). For a policy in band B with exposure 0.5 years, β0 = 1.0 and β1 = 0.4. What is the fitted expected number of claims?
The fitted expected claims are about 2.03. The log of exposure is an offset, so the mean is exposure times exp(β0 + β1). That is 0.5 × e^1.4, or 0.5 × 4.055, approximately 2.03.
- A4.06
- B2.03Correct
- C2.72
- D1.35
- 3.00
Explanation
The log(exposure) term is an offset with coefficient fixed at 1. So μ = exp(1.0 + 0.4) × 0.5 = 4.055 × 0.5 ≈ 2.03. Option 4.06 ignores the offset, the usual mistake.
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