R help - Feb 2003 - Covariance matrix for GMM

Hey, All

Now I generate a data vector X (d-dimension column vector) from a Gaussian
Mixture Model (GMM).
That is, the pdf of vector X is
f(X) = a1*N(u1, Cov1) + a2*(u2, Cov2)
where a1+a2 = 1, N is multidimensional normal distribution, ui is the mean
vecotr, Covi is the covariance matrix, i=1, 2.

So can I get the close forms of the mean and covariance matrix for the
random vector X?

Thanks very much.

Fred

There is no way to answer this question?

even for writing the sample covariance matrix
formulation for the data set [X, Y] where
X(n observations) and Y (m observations) are from
the class 1 and class 2 which both are
multidimensional normal distribution?


----- Original Message -----
From: "Feng Zhang" <f0z6305 at labs.tamu.edu>
To: "R-Help" <r-help at stat.math.ethz.ch>
Sent: Tuesday, February 11, 2003 12:11 AM
Subject: [R] Covariance matrix for GMM

> Hey, All
>
> Now I generate a data vector X (d-dimension column vector) from a Gaussian
> Mixture Model (GMM).
> That is, the pdf of vector X is
> f(X) = a1*N(u1, Cov1) + a2*(u2, Cov2)
> where a1+a2 = 1, N is multidimensional normal distribution, ui is the mean
> vecotr, Covi is the covariance matrix, i=1, 2.
>
> So can I get the close forms of the mean and covariance matrix for the
> random vector X?
>
> Thanks very much.
>
> Fred
>
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> R-help at stat.math.ethz.ch mailing list
> stat.math.ethz.ch/mailman/listinfo/r-help