Hi,

Charles R Harris wrote:

>

> On Thu, Jul 23, 2009 at 7:14 AM, per freem <

[hidden email]
> <mailto:

[hidden email]>> wrote:

>

> i'm trying to find the function for the pdf of a multivariate normal

> pdf. i know that the function "multivariate_normal" can be used to

> sample from the multivariate normal distribution, but i just want to

> get the pdf for a given vector of means and a covariance matrix. is

> there a function to do this?

>

> Well, what does a pdf mean in the multidimensional case? One way to

> convert the density function into a Stieltjes type measure is to plot

> the integral over a polytope with one corner at [-inf, -inf,....] and

> the diagonally opposite corner at the plotting point, but the

> multidimensional display of the result might not be very informative.

> What do you actually want here?

You are confusing PDF (Probability Density Functions) with CDF

(Cumulative Density Function), I think. The PDF is well-defined for

multivariate distributions. It is defined so that P(x) dx is the

probability to be in the infinitesimal range (x,x+dx).

For a multivariate gaussian, it's

P(x|m, C) = [1/det(2 pi C)] exp{ -1/2 (x-m)^T C^{-1} (x-m) }

in matrix notation, where m is the mean and C is the covariance matrix.

Andrew

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