I propose to add the full Tweedie family into the GeneralizedLinearRegression model. The Tweedie family is characterized by a power variance function. Currently supported distributions such as Gaussian, Poisson and Gamma families are a special case of the Tweedie.
I propose to add support for the other distributions:
- compound Poisson: 1 < variancePower < 2. This one is widely used to model zero-inflated continuous distributions.
- positive stable: variancePower > 2 and variancePower != 3. Used to model extreme values.
- inverse Gaussian: variancePower = 3.
The Tweedie family is supported in most statistical packages such as R (statmod), SAS, h2o etc.