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.