Power parameter in the Tweedie family that corresponds to a gamma/exponential distribution.

Power parameter in the Tweedie family that corresponds to a gamma/exponential distribution.

• A. 3
• B. 2
• C. 0
• D. 1

Answer: (B)

In Tweedie models, the variance of the response is linked to the mean by Var(Y) = φ μ^p, so the power parameter p sets how the variance grows with the mean. Gamma and exponential distributions both have variance that grows with the square of the mean, i.e., Var(Y) ∝ μ^2. That corresponds to p = 2. The other values map to different distributions: p = 0 gives a normal with constant variance, p = 1 gives a Poisson with Var(Y) = μ, and p around 3 relates to the inverse Gaussian family within the Tweedie class. So p = 2 is the correct match for gamma/exponential.

In Tweedie models, the variance of the response is linked to the mean by Var(Y) = φ μ^p, so the power parameter p sets how the variance grows with the mean. Gamma and exponential distributions both have variance that grows with the square of the mean, i.e., Var(Y) ∝ μ^2. That corresponds to p = 2. The other values map to different distributions: p = 0 gives a normal with constant variance, p = 1 gives a Poisson with Var(Y) = μ, and p around 3 relates to the inverse Gaussian family within the Tweedie class. So p = 2 is the correct match for gamma/exponential.