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I've got several series of random data, which can be denoted as x1,x2,...,xn. How do I show that they are subjected to multivariate normal distribution?
I refered to statistics textbooks but only got definations and properties. Do I have to estimate their density functions? Or is there any other necessary conditions?
Thanks in advance!

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You are asking two different questions:

How do I show the data originates from a normal distribution?

This is as always a nontrivial question. Usually we compare two hypothesis and can show which one is more likely, and that is when you need to provide some furthe assumptions on the distributions you'd want to consider.

But again Wikipedia has some answers.

How do I estimate the parameters of a normal distribution.

It depends on what method you are using (you can google those easily). If you're going to go with a maximum likelihood estimation the formula are given on Wikipedia (in this case ML estimators are just mean/covariance matrix)

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  • $\begingroup$ Thank you @flawr. That's very detailed. In my case, each x1~xn seems to be normal distribution viewed from graphs, I'm considering to integrate them. So I guess it's about the first question you mentioned. $\endgroup$
    – Liu
    Apr 14, 2016 at 3:13

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