Sarah Sanchez <sarah_sanchez09 <at> yahoo.com> writes: > > Dear R helpers > > I am working on the Bi-variate Normal distribution probabilities. > I need to double integrate the following function > (actually simplified form of bivariate normal distribution) > > f(x, y) = exp [ - 0.549451 * (x^2 + y^2 - 0.6 * x * y) ] > > where 2.696 < x < 3.54 and -1.51 < y < 1.98 > > I need to solve something like > > INTEGRATE (2.696 to 3.54) dx INTEGRATE [(-1.51 to 1.98)] f(x, y) dy > > I have referred to stats::integrate but it deals with only one variable. > > This example appears in Internal Credit Risk Model by Michael Ong > (page no. 160).
There has been the same request last month, the answer is still valid: library(cubature) fun <- function(x) exp(-0.549451*(x[1]^2+x[2]^2-0.6*x[1]*x[2])) adaptIntegrate(fun, c(-1.51,1.98), c(2.696,3.54), tol=1e-8) # $integral # [1] 0.1376102 # $error # [1] 1.372980e-09 # ... Hans Werner > > Kindly guide. > > Regards > > Sarah > ______________________________________________ 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.