Tweedie Distribution for Aggregate Claims Modeling

What Is the Tweedie Distribution?

The Tweedie distribution is a member of the exponential dispersion family characterized by a power variance function: the variance is proportional to the mean raised to power p. For p between 1 and 2, the Tweedie distribution is a compound Poisson-gamma model, making it ideal for insurance aggregate claims. It naturally handles the point mass at zero (policies with no claims) and the continuous positive distribution (total claim amounts for policies with claims). This eliminates the need to separately model frequency and severity, allowing actuaries to model pure premium directly.

Practical Applications

Using a Tweedie GLM for insurance pricing simplifies the modeling process by combining frequency and severity into a single model. The power parameter p can be estimated from the data or set based on actuarial judgment. Values of p closer to 1 emphasize frequency, while values closer to 2 emphasize severity. The Tweedie approach is particularly useful when the actuary suspects interactions between frequency and severity, as a single model captures these effects naturally. Implementation is straightforward in R (using the tweedie or statmod packages) and Python (using statsmodels or scikit-learn).