ENH: frontier model, convolution distribution

[josef-pkt]

parking an issue for another category of models that could be handled by generic multi-link models, models with multiple distribution parameters

example exponentially modified gaussian distribution, available in scipy as exponnorm.
wikipedia page mentions use in stochastic frontier analysis
https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution#Occurrence

https://stats.stackexchange.com/questions/643241/constructing-a-generalized-linear-model-when-the-dependent-variable-has-a-expone/643320#643320 answer with references in biostatistics.

AFAIR, Greene has a book or long article on frontier models, but I never looked at more than the basic idea.

advantage of exponnorm: pdf has explicit form (using scipy special)

not so easy for distributions without explicit loglike:
AFAIR, generic convolution requires numerical integration or inversion of characteristic function
(e,g, #8754 for characteristic function inversion, I stopped looking at that a long time ago, but I should still have old code for it.
The main problem, AFAIR, was figuring out required tolerance in the numerical inversion especially for tail behavior in risk analysis, which was my topic at the time. It should be easier if we are mainly interested in the main, central part of the distribution.)

Related:
AFAIR, I also used Quantile regression in experiments to get something similar as a baseline or "frontier" model.
Also, outlier robust methods, like RLM might work for this, including M-quantiles.)