ENH/SUMM MLE based mean-variance models

[josef-pkt]

I would like to get fully specified MLE models for mean-variance models, e.g. we don't have HetGaussian yet, just HetGLS, another case Beta regression and I guess we can add a variance function to GeneralizedPoisson, Another possible case is Gamma for which there exist some example scripts as MLE and as GMM.

What I would like are different cases for score/LM or CM test for joint or separate mean and variance hypothesis, see #4729

This is specific for MLE cases, we have separate issues for QMLE or GMM or sequential/iterative estimators in GLM/LEF (like HetGLS extended to HetGLM).

Another one that I bookmarked but never looked at closely: BetaBinomial as dispersed Binomial.