[SciPy-Dev] Tweedie distributions in scipy.stats

[Christian Lorentzen]

Dear Scipy Developers and mailing list Readers

I'd like to address the issue [1] to implement Tweedie distributions [2] 
in scipy.stats.

Purpose
The family of Tweedie distributions contains many known distributions 
like the Poisson and the Gamma distribution, but also distributions 
between them, aka compound poisson gamma distribution, see [3]. These 
are often appropriate for insurance claims and other fields, where one 
has a (Poisson) random count process of events and every event has a 
(Gamma) random size/amount.
The distribution would enable simulations, maximum likelihood estimation 
of all parameters, choice and visualization of distributions, etc.

Implementation
I started PR [4] for Wrights generalized Bessel functions as a private 
function in scipy.special.
Once this is ready, the pdf follows immediately.
For the range of interest of Y ~ compound poisson gamma distribution, 
the distribution of Y has a point mass at zero and is otherwise 
continuous for Y>0.
As already discussed in the issue [1], Tweedie might best fit as 
|rv_generic|.
As such, it would be the first one, all others are either |rv_discrete| 
or |rv_continuous|.
Without a template, I would need guidance how to implement a new rv_generic.

References:
[1] https://github.com/scipy/scipy/issues/11291
[2] https://en.wikipedia.org/wiki/Tweedie_distribution
[3] https://en.wikipedia.org/wiki/Compound_Poisson_distribution
[4] https://github.com/scipy/scipy/pull/11313

I'm looking forward to your feeback, thoughts and insights.


Kind regards,
Christian

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