search

ChaoranHu / coga

R package for Convolution of Gamma Distributions
GNU General Public License v3.0
4 stars 1 forks source link

Likelyhood fitting #3

Closed lrnv closed 1 year ago

lrnv commented 5 years ago

Hey,

Do you now if there exist somewhere an algorithm to fit gamma convolutions to data ? For exemple with a fixed number of gamma random variable.

ChaoranHu commented 1 year ago

Sorry for the very late reply, @lrnv! Just in case you still need this information, we do not have an analytical formula for this question. So, the optimization can be done by common numerical way.

--C.Hu

lrnv commented 1 year ago

Hey ! Thanks for reaching out. Funny enough, I forgot about the very existence of this issue... but not about the problem itself: I ended up extensively answering the question myself and this made the core of my PhD.

To put it in a nutshell, common maximization of the coga likelihood will not work due to instabilities. I developed a few better estimation methods for these models, together with a lot of theoretical analysis about the class of (multivariate) generalized gamma convolutions, with a few outputs that might be of interest to you if you still study the Thorin classes:

Sadly, I was not able to leverage R::coga for precision issues (details in paper 1), and I had to reimplement it (along a lot of other things) in Julia to get acess to higher precision computations. But nevertheless, I thought this might be interesting for you.