Given likelihood of gamma (external approximation convoluted gamma) calculate likelihood of NB

[bnicenboim]

I played a little bit with the difference of gamma distributions.

Optimization of a custom likelihood --when is it worthwile to code it in C++ with its derivative?

Hi, I wrote the likelihood for the difference between two gamma distributions with the same rate using the saddle point approximation (thanks to @martinmodrak’s blog post!). I could find an analytical solution to the approximation, and here it is below. The thing is that it’s quite slow (~10 mins for 1000 observations), and I don’t think it can be optimized further (I’ll be happy to be proved wrong). Will I gain a significant speedup if I code it in c++ with its derivative? (I’m not fluent in …

The saddle approximation has an analytical solution for the convolution of two gammas.