Hi I have a prob here I hope you can help. Let N_a(x) denote Gaussian
distribution with mean mu_a and cov_a (the subscript indicates the index of
the distribution). Given a mixture of two gaussians distribution,
p(b)N_b(x) + p(c)N_c(x), I'd like to the integral

int[ N_a(x) log(p(b) N_b(x) + p(c)N_c(x)) , dx]

Matlab can't solve this. Very grateful if you can find at least an
approximation to this problem.

Zeke
KEDRI, AUT, New Zealand

In article ,
Zeke Chan wrote:
Hi I have a prob here I hope you can help. Let N_a(x) denote Gaussian
distribution with mean mu_a and cov_a (the subscript indicates the index of
the distribution). Given a mixture of two gaussians distribution,
p(b)N_b(x) + p(c)N_c(x), I'd like to the integral

int[ N_a(x) log(p(b) N_b(x) + p(c)N_c(x)) , dx]

Matlab can't solve this. Very grateful if you can find at least an
approximation to this problem.

Perhaps some clarifications might be helpful. By N_a(x) do you mean the
density of a (one-variable) Gaussian distribution? And are you
integrating from -infinity to infinity?

I doubt that there's a closed-form formula for the answer. If you want
an approximation, useful asymptotic results may be possible. But
you'd need to tell us which parameters are to be considered
small (- 0) or large (- infinity).

Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2