Double integral: fvec = function(x, y) sapply(x, function(z, y) dnorm(y, mean=0.75/z) * dnorm(z, mean=0.6, sd=0.15), y=y)
gvec = function(x) sapply(x, function(y) integrate(f, lower=-Inf, upper=Inf, y=y, subdivisions=10000, rel.tol=1.e-08)$val) xx <- seq(-5, 5, length=1000) plot(xx, gvec(xx), type="l") > integrate(gvec, lower=-Inf, upper=Inf, subdivisions=10000, rel.tol=1.e-06) 0.999914 with absolute error < 5.7e-07 > integrate(gvec, lower=0, upper=Inf, subdivisions=10000, rel.tol=1.e-06) 0.8954554 with absolute error < 9.4e-07 > Ravi. ____________________________________________________________________ Ravi Varadhan, Ph.D. Assistant Professor, Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University Ph. (410) 502-2619 email: rvarad...@jhmi.edu ----- Original Message ----- From: Carrie Li <carrieands...@gmail.com> Date: Wednesday, June 23, 2010 8:23 pm Subject: Re: [R] integrate dmvtnorm To: Christos Argyropoulos <argch...@hotmail.com> Cc: r-help@r-project.org > Thanks! > Both suggestions are very helpful. > One more question: > Can I use Vectorize to solve double integration question ? > > Now that > f=function(x, y) {dnorm(y, mean= 0.75/x)*dnorm(x, mean=0.6, > sd=0.15)} > > And I want to integrate x first,then y. Ravi used sapply, which is > good, but > it seems to be that Vectorize is easier. > > Thanks for help. I appreciated > > Carrie > > 2010/6/23 Christos Argyropoulos <argch...@hotmail.com> > > > No something else is going on here .... > > > > > > f=function(x) {dmvnorm(c(0.6, 0.8), mean=c(0.75, 0.75/x))*dnorm(x, > > mean=0.6, > > sd=0.15)} > > > > > f(1) > > [1] 0.01194131 > > > > > x<-seq(-2,2,.15) > > > f(x) > > > > Error in dmvnorm(c(0.6, 0.8), mean = c(0.75, 0.75/x)) : > > mean and sigma have non-conforming size > > > > But ... > > > > > sapply(x,f) > > [1] 1.205791e-66 2.377822e-59 1.712003e-52 4.488794e-46 4.269526e-40 > > [6] 1.464321e-34 1.793031e-29 7.702766e-25 1.122712e-20 5.165600e-17 > > [11] 6.242351e-14 1.074366e-11 8.904914e-12 2.165575e-59 2.892453e-13 > > [16] 2.446326e-03 9.655456e-02 3.377855e-01 3.230318e-01 1.040144e-01 > > [21] 1.194131e-02 4.984067e-04 7.620137e-06 4.281072e-08 8.849889e-11 > > [26] 6.735400e-14 1.887638e-17 > > > > > > suggesting the solution: > > > > vf<-Vectorize(f) > > > > > integrate(vf,lower=-Inf, upper=Inf) > > > > 0.1314427 with absolute error < 4e-05 > > > > > > Christos > > > > > > > > > > > Date: Wed, 23 Jun 2010 19:05:53 -0400 > > > From: carrieands...@gmail.com > > > To: R-help@r-project.org > > > Subject: [R] integrate dmvtnorm > > > > > > > > Hello, everyone, > > > > > > I have a question about integration of product of two densities. > > > Here is the sample code; however the mean of first density is a function > > of > > > another random variable, which is to be integrated. > > > > > > ## > > > f=function(x) {dmvnorm(c(0.6, 0.8), mean=c(0.75, 0.75/x))*dnorm(x, > > mean=0.6, > > > sd=0.15)} > > > integrate(f, lower=-Inf, upper=Inf) > > > > > > ## error message > > > Error in dmvnorm(c(0.6, 0.8), mean = c(0.75, 0.75/x)) : > > > mean and sigma have non-conforming size > > > > > > I think it's because the mean in dmvnorm is a function of x.... > > > > > > is there any package or function to handle this question ? > > > > > > Thanks for any help! > > > > > > Carrie > > > > > > [[alternative HTML version deleted]] > > > > > > ______________________________________________ > > > R-help@r-project.org mailing list > > > > > > PLEASE do read the posting guide > > > > > and provide commented, minimal, self-contained, reproducible code. > > > > ------------------------------ > > Your E-mail and More On-the-Go. Get Windows Live Hotmail Free. Sign > up > > now. <> > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > > PLEASE do read the posting guide > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ 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.