Re: Multivariate pdf of a normal distribution

[Mike Miller]

On Sat, 5 Nov 2005, Paul Kienzle wrote:

> The math looks pretty easy to implement:
>
>         http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc542.htm
>
> Using Cholesky factorization on the positive definite covariance matrix:

why not this?:

density = mvnorm_pdf(x, mu, Sigma)

# first check array sizes, but I'm skipping that

p = length(x);

density = (2*pi)^(-p/2) * (1/sqrt(det(Sigma))) * 
exp(-.5*(x-mu)'*inv(Sigma)*(x-mu));


Of course, the density goes to infinity when Sigma is singular.  Is your 
use of chol() just meant to check that the matrix is PD?


Mike



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