How to compute this double integral in r? - r

Question

I'm wanting to compute an integral of the following density function :
Using the packages "rmutil" and "psych" in R , i tried :
X=c(8,1,2,3)
Y=c(5,2,4,6)
correlation=cov(X,Y)/(SD(X)*SD(Y))
bvtnorm <- function(x, y, mu_x = mean(X), mu_y = mean(Y), sigma_x = SD(X), sigma_y = SD(Y), rho = correlation) {
force(x)
force(y)
function(x, y)
1 / (2 * pi * sigma_x * sigma_y * sqrt(1 - rho ^ 2)) *
exp(- 1 / (2 * (1 - rho ^ 2)) * ((x - mu_x) / sigma_x) ^ 2 +
((y - mu_y) / sigma_y) ^ 2 - 2 * rho * (x - mu_x) * (y - mu_y) /
(sigma_x * sigma_y))
}
f2 <- bvtnorm(x, y)
print("sum_double_integral :")
integral_1=int2(f2, a=c(-Inf,-Inf), b=c(Inf,Inf)) # should normaly give 1
print(integral_1) # gives Nan
The problem :
This integral should give 1 , but it gives Nan ??
I don't know how can i fix the problem , i tried to force() x and y variables without success.

Answer 1

You were missing a pair of parentheses. The corrected code looks like:
library(rmutil)
X=c(8,1,2,3)
Y=c(5,2,4,6)
correlation=cor(X,Y)
bvtnorm <- function(x, y, mu_x = mean(X), mu_y = mean(Y), sigma_x = sd(X), sigma_y = sd(Y), rho = correlation) {
function(x, y)
1 / (2 * pi * sigma_x * sigma_y * sqrt(1 - rho ^ 2)) *
exp(- 1 / (2 * (1 - rho ^ 2)) * (((x - mu_x) / sigma_x) ^ 2 +
((y - mu_y) / sigma_y) ^ 2 - 2 * rho * (x - mu_x) * (y - mu_y) /
(sigma_x * sigma_y)))
}
f2 <- bvtnorm(x, y)
print("sum_double_integral :")
integral_1=int2(f2, a=c(-Inf,-Inf), b=c(Inf,Inf)) # should normaly give 1
print(integral_1) # prints 1.000047
This was hard to spot. From a debugging point of view, I found it helpful to first integrate over a finite domain. Trying it with things like first [-1,1] and then [-2,2] (on both axes) showed that the integrals were blowing up rather than converging. After that, I looked at the grouping even more carefully.
I also cleaned up the code a bit. I dropped SD in favor of sd since I don't see the motivation in importing the package psych just to make the code less readable (less flippantly, dropping psych from the question makes it easier for others to reproduce. There is no good reason to include a package which isn't be used in any essential way). I also dropped the force() which was doing nothing and used the built-in function cor for calculating the correlation.