I was wondering if PyMC is planning on adding new distributions. I’m particularly interested in a continuous distribution which is a generalized normal distribution that has parameters for both skewness and kurtosis.
I am particularly thinking of the SHASH family (check this). So my first question is whether there are plans to add such distributions.
And my second question is a follow-up of the first one. I have heard that one could use any arbitrary distributions by creating new classes. Could anyone explain what functions/methods are required to define a new distribution (e.g. I can think of dist() and logp(), but am not sure about the complete set).
I should also note that I would like the distribution to be compatible with PyMC’s implementation of ADVI, so if ADVI requires any particular additional methods please also let me know.
P.S. to provide more context, I’m thinking of implementing a type of non-gaussian hierarchical bayesian regression similar to what’s described here