Question

Problem

I have computed a probability density function that depends on two variables. I want to use this multivariate distribution to generate some random numbers that occur with a probability proportional to the PDF.

As it seems, SciPy currently only supports univariate distributions. Are there any simple methods or easy-to-use packages that allow 2d-distributions?

As a workaround, I might try creating random numbers on the domain of interest and throwing them away or keeping them with a chance related to my PDF, but still there might be other options. The random number generation does not have to be fast.

Thanks for your help!

Here’s a possible solution

Based on the answers (thanks a lot!), I hacked in some code the you may find in this gist. If you run this example with a sin^2*Gauss PDF, 2000 random random variates that fulfil a given condition (be inside a circle) will be plotted over the PDF. Maybe that’s helpful for others, too.

Answer 1

So you have a PDF F(x,y) and you want to generate the pairs of x and y distributed according to this PDF?

I’d say unless you can use the multivariate version of the inversion technique (wiki), the rejection sampling is the way to go.