I’ve been working on the Levy alpha-stable distribution and was wondering if I could use Stan to fit this model. The issue is that a general stable distribution does not have a closed form PDF but has quite a complicated characteristic function.

This means that every time the likelihood is evaluated, there should be a numerical integration. Would it be feasible to implement this function in Stan?

I tried several times without much success although without a definitive failure. @randommm has implemented a numerical integrator that I think is or is close to being merged into Stan, in which case you could use the same (fairly well-behaved) integral expression that Nolan uses. Also, you introduce N latent variables and use Buckle’s approach where the stable distribution is one margin of a bivariate distribution with a closed form PDF.

Thank you so much for your kind reply. It looks like quite hard to implement it in Stan. I’ll give it a shot and let you know if I see any progress. Thanks again for all your inputs.