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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

An actuary models average claim severity for motor own-damage claims, which are positive and right-skewed with variance roughly proportional to the square of the mean. Which GLM specification is most appropriate?

A gamma distribution with a log link is most appropriate. Gamma has variance proportional to the mean squared, is positive and right-skewed, and the log link ensures positive fitted means and multiplicative rating factors, which suits claim severity.

  1. AGamma distribution with log linkCorrect
  2. BPoisson distribution with log link
  3. CNormal distribution with identity link
  4. DBinomial distribution with logit link
  5. Inverse Gaussian distribution with identity link

Explanation

Gamma has variance proportional to mean squared (constant coefficient of variation), is positive and skewed, and the log link keeps means positive and gives multiplicative effects. Poisson suits counts, normal allows negatives, binomial suits proportions, and inverse Gaussian has variance proportional to mean cubed.

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