Tweedie Distribution

The Tweedie distribution is actually a family of distributions belonging to the class of exponential dispersion models such that the variance is of the form Var(Y) = φμP, where φ > 0 is the dispersion/scale parameter and μ is the mean. P must be in the interval (-∞, 0] U [1, ∞).

In STATISTICA, you can specify Tweedie as a distribution for a generalized linear model with the index parameter between 1 and 2. This allows you to model a distribution that is continuous for values greater than 0 with a mass at 0. This type of mixture distribution is also called a Poisson-Gamma distribution.

This distribution is common in the insurance industry. For example, let k be the number of claims of a policy and let y1, y2, …, yk be the amounts of each individual claim. The total claim size is the sum:

with Z=0 if k=0. If k varies according to a Poisson distribution and the ys are independent gamma random variables, then Z varies according to the Tweedie distribution.