Add Lambert W x F distributions to XGBoostLSS

[gmgeorg]

Adds skewed and tail Lambert W x F distributions as an option to XGBoostLSS.

In particular, adds Lambert W x {Normal, Weibull, Gamma, Exponential, LogNormal} distributions. Adds examples to notebooks and adds its own California Housing example notebook.

[StatMixedML]

@gmgeorg Thanks for creating the PR.

I assume you further refine the notebooks and the .py files? Since, e.g., the Gaussian example still has some explanations for modelling the gaussian distribution whereas it should explain the Lambert W x F distributions. Also, result wise, the gaussian example notebook does not look good.

[gmgeorg]

@StatMixedML yes will clean up. However, I wanted to send this out first as a general "it works" proof of concept PR. If this looks good to you high level with the current changes, I will continue and
a) clean up .py files
b) update notebooks accordingly
c) fix / add unit tests based on the changes made (in particular dist_select() and changing the 1:1 map between filenames and distribution names to allow for more than 1 distribution class per file)

Let me know if I should revisit/re-implement differently any proposed changes; if not, will go ahead and clean up rest of PR for a e2e review.

[gmgeorg]

@StatMixedML updated PR with changes addressing earlier points. PTAL

[fkiraly]

@gmgeorg, would you be interested adding some distributions to skpro?

See proposed integration issue here: sktime/skpro#184

Integration with skpro would pull all the way through to sktime.

[gmgeorg]

@fkiraly Great idea! Will take a look and add an issue there.

[gmgeorg]

@StatMixedML What's the status here? I'd like to move this along as impelmentation and tests conform to rest of XGB lss. Anything else you want to have added?