G-and-k distributions with skewness and kurtosis


I’ve just started googling, so I have no prior knowledge to that topic. I am looking for a parametric (ideally 4 parameters) distribution with which I can model high moments like skewness and kurtosis.

I’ve found some references in a topic area Approximate Bayesian Computational methods (ABC methodology) that talk about g-and-k distributions. The following tutorial is a quick intro:

Does somebody know how to use such a g-and-k distribution in PyMC3? Or alternatively: does somebody know of another way that works in PyMC3 with which I can model a parametric distribution with higher moments?

Thanks a lot!

1 Like

Hi Christian,
I’m not versed in that area, but I know @aloctavodia works on the SMC-ABC sampler in PyMC3, so maybe he’ll be able to give you some pointers?
This is a long shot though, since, again, I don’t know this area :man_shrugging:

Hi @cs224,

PyMC3 has a skewed normal distribution. And you also have the student t distribution. But I guess what you want is a skewed t distribution, unfortunately that distribution is not included with PyMC3, but you still can create it and use it with the help of pm.DensityDist.


You could try a Normal with SinhArcsinh transformation. Again that isn’t available in PyMC3 so would require coding yourself.

Thank you all for your replies. For the moment I’ve decided to go with the gk R package: https://github.com/dennisprangle/gk