Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

In a Poisson GLM, an observation has y = 9 and fitted mean μ = 4. Compute the Pearson residual and the deviance residual. Which pair is correct (to two decimals)?

The Pearson residual is (9−4)/√4 = 2.50. The unit deviance is 2[9 ln(9/4) − 5] ≈ 4.597, so the deviance residual is its positive square root, about 2.14. The pair 2.50 and 2.14 is therefore correct.

  1. APearson 2.50, deviance 2.14Correct
  2. BPearson 2.50, deviance 2.58
  3. CPearson 1.25, deviance 2.14
  4. DPearson 5.00, deviance 2.14
  5. Pearson 2.50, deviance 4.58

Explanation

Pearson = (9−4)/√4 = 2.50. Unit deviance d = 2[9 ln(9/4) − (9−4)] = 2[9×0.81093 − 5] = 2[7.2984 − 5] = 4.5968. Deviance residual = +√4.5968 = 2.144. Pearson dividing by μ instead of √μ would give 1.25, a wrong-base error.

Did you get it right without looking?

One question tells you little. A timed set on Generalised linear models shows your real accuracy, how long you take and where you lose marks.

Practise Generalised linear modelsFree diagnostic mock

More Generalised linear models questions