"sam Zughni" <samirzughni@gmail.com> wrote in message <i4gr3b$n37$1@fred.mathworks.com>...
> hi, im stuck on a problem and looking for a bit of help. I have a bivariate normal distribution mean= [0, 0] , and standard deviation equal in x and y directions. Im trying to find a function or routine that will return the cumulative normal as a function of radius or distance form [0, 0]. i think mvncdf is only good to me for square regions. any clue on how to do this?
         
You didn't say whether the two distributions are independent. Assuming that they are and assuming that by "cumulative normal" you mean the probability that both distributions lie inside a circle with center (0,0) and radius r, then you can find it by doing the integration. The answer will be
P(x^2+y^2<=r^2) = 1  exp(r^2/(2*sigma^2))
This comes from the double integral of p(x)*p(y) taken over the circle x^2+y^2<=r^2 where p(x) and p(y) are the two pdf's. You change variables from x and y to polar coordinates and you have integrals that are easy to solve directly by calculus methods.
Roger Stafford
