statistics - How to approximate a 2d distribution with mu and covariance in python

Question

I want to create a heatmap, depending on just the mu and the covariance. The background is, that I want to approximate a specific complex distribution with just these two parameters. I don't want to sample from these distribution, but assign values between 0 and 1, while at mu the value should be 1.

I already found a way to use the precision matrix for that purpose, i.e. approximate using the first two moments:

In this equation, u refers to a specific coordinate. Can anyone explain me, how this is done with the covariance matrix? Is there maybe an easy way to do this in python?

The heat maps I want to generate look as follows:

question from:https://stackoverflow.com/questions/65848422/how-to-approximate-a-2d-distribution-with-mu-and-covariance-in-python

Answer 1

Waitting for answers