Thanks Jay. I realized that I was doing it a silly way shortly after I posted and that the answer i was looking for is simply
condXY(y, x, my, mx, r) * dnorm(y, my) condXY <- function(y, x, my, mx, r) { m <- mx + r*(y - my) s <- sqrt(1-r^2) p <- 1 - pnorm(x, mean=m, sd=s) + pnorm(-x, mean=m, sd=s) } On Wed, Oct 1, 2008 at 1:11 PM, G. Jay Kerns <[EMAIL PROTECTED]> wrote: > Dear Sasha, > > On Wed, Oct 1, 2008 at 11:43 AM, Sasha Pustota <[EMAIL PROTECTED]> wrote: >> Package mvtnorm provides dmvnorm, pmvnorm that can be used to compute >> Pr(X=x,Y=y) and Pr(X<x,Y<y) for a bivariate normal. >> >> Are there functions that would compute Pr(X<x,Y=y)? >> I'm currently using "integrate" with dmvnorm but it is too slow. > > > Strictly speaking, the probability that you are asking to calculate is > always 0, for every value of y. The reason is that the quantity you > are requesting is the _volume_ of a vertical slice, at the value y, > which is zero. It may be useful to think carefully about the problem > you are trying to solve... perhaps a conditional probability is more > appropriate. > > You did not say exactly which integral you are trying to compute: > conceivably it would be > > \int_{-\infty}^{x} f(u, y) du, > > where f(.,.) is the bivariate normal pdf. If this is indeed what you > want, then a work-around would be to calculate P( X < x | Y = y ). We > know that given Y=y, X is normal with mean and variance formulas given > in most introductory statistics books. Thus, you could compute P( X < > x | Y = y ) with pnorm(x, mean = something, sd = something). > > In that case, the integral above would simply be P( X < x | Y=y ) * > f(y), where f(y) is the marginal pdf of Y (a dnorm). > > Note that the above is assuming that y is a fixed constant; if not, > then you may want to check out the Ryacas package. > > I hope that this helps, > Jay > > > > > > *************************************************** > G. Jay Kerns, Ph.D. > Associate Professor > Department of Mathematics & Statistics > Youngstown State University > Youngstown, OH 44555-0002 USA > Office: 1035 Cushwa Hall > Phone: (330) 941-3310 Office (voice mail) > -3302 Department > -3170 FAX > E-mail: [EMAIL PROTECTED] > http://www.cc.ysu.edu/~gjkerns/ > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.