Casualty Actuarial Society MAS-1 Practice Exam

In the Tweedie family, the variance of the response is linked to the mean by Var(Y) = φ μ^p. When p is zero, μ^p becomes 1, so the variance is constant: Var(Y) = φ regardless of the mean. A constant-variance model is exactly the Normal distribution with a fixed dispersion parameter, which is why p = 0 corresponds to a Normal distribution. The other options require the variance to grow with the mean (or with higher powers of the mean): Poisson has Var ∝ μ, Gamma has Var ∝ μ^2, and the inverse-Gaussian relates to an even stronger mean-variance relationship. Hence the Normal is the correct match for p = 0.