Statistical distribution comparison for two datasets

For example I have two multivariate random variables a and b, and for a and b, I have N realizations for both of them such as and . I do not know the exact distribution of a and b, and I would like to know if they are approximately following the same distribution. Is there any method I can do that?

Answer 1

[Jeff Miller]

You could use manova if you just wanted to compare the centroids of the multivariate distributions, but it sounds like you want more than that--i.e., the ability to detect any sort of differences in the distributions, not just centroids.

If that is the case, you might be able to use a multivariate generalization of tests for full distributions.

I hope your N is huge...

Answer 2

[KSSV]

Plot histogram

[Kevin Zhu]

The dataset is in high-dimension, I don't think I can visually compare it.......

[KSSV]

What dimension it is? You can specify the number of bins.

[Kevin Zhu]

Consider a is a 100-dimension multivariate random variable, and I have dataset with N realizations. What I want to compare is the random aand b. I'll make it clear in the question