pbivnorm is an R package containing a vectorized function to compute the
bivariate normal CDF. It is based on
the mnormt package
by Adelchi Azzalini, which uses
Fortran code by Alan Genz to
compute integrals of multivariate normal densities.
A call to pbivnorm() produces identical output to a corresponding set of
calls to mnormt::pmnorm(), but at lower computational cost due to
vectorization (i.e., looping in Fortran rather than in R).
R> library("pbivnorm")
R> library("mnormt")
R> set.seed(9497)
R> x1 <- rnorm(10)
R> x2 <- rnorm(10)
R> X <- cbind(x1, x2)
R> all.equal(pbivnorm(X), apply(X, 1, pmnorm, mean = c(0, 0), varcov = diag(2)))
## [1] TRUE
R> library("microbenchmark")
R> microbenchmark(pbivnorm = pbivnorm(X),
mnormt = apply(X, 1, pmnorm, mean = c(0, 0), varcov = diag(2)))
## Unit: microseconds
## expr min lq median uq max neval
## pbivnorm 59.373 61.851 66.987 73.373 140.38 100
## mnormt 1052.671 1074.699 1091.472 1120.907 2283.88 100