Vectorized bivariate normal CDF in R
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Vectorized bivariate normal CDF

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