# subtraction of two multivariate normal distribution [duplicate]

Assume that we have a $n$-dimensional vector that shows the position of a point and two multivariate normal distributions with means $\mu_1$ and $\mu_2$, and covariances $cov_1$ and $cov_2$.

I’m trying to find a formula to calculate the subtraction of the distance between that point and each of those multivariate normal distributions.

Or if let me know how can I have subtraction of two different multivariate normal distribution.

I'd be really thankful if someone explain it for me.

• Please consider this: en.wikipedia.org/wiki/… If I understand your question properly, it is easily searchable on the internet. – sashkello Apr 15 '13 at 5:19
• Thank you very much for your kindly response. However I suppose that there are some different between my question and that wikipedia address. – user65713 Apr 17 '13 at 7:11
• Then formulate your question in a way so that it is understandable what the problem is. – sashkello Apr 17 '13 at 8:08