IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
In a Poisson GLM with canonical log link, the observed counts are y = 2, 4, 6 for three observations that share a single intercept-only model, log(mu) = beta0. What is the maximum likelihood estimate of mu?
The maximum likelihood estimate of mu is 4. With a canonical log link and only an intercept, the score equation sets the sum of observed counts equal to the sum of fitted means, so mu equals the sample mean, 12 divided by 3.
- A3
- B4Correct
- C4.5
- D2.4
- 6
Explanation
The score equation for the intercept in the Poisson model with log link is sum(y - mu) = 0. This gives 3*mu = 12, so mu = 4 and beta0 = log 4. The value 3 would result from dividing by the wrong count, and 4.5 is the median-type or incorrect average.
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