`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
```