## Standard bivariate normal CDF

### Description

Calculate probabilities from the CDF of a standard bivariate normal distribution.

### Usage

`pbivnorm(x, y, rho = 0, recycle = TRUE)`

### Arguments

`x` |
vector of upper integration limits for the CDF. May also be a
two-column matrix, in which case |

`y` |
vector of upper integration limits. |

`rho` |
correlation parameter. |

`recycle` |
whether to automatically recycle the vectors |

### Details

This function returns values identical to those of `biv.nt.prob`

in the
mnormt package, but is vectorized to reduce the number of Fortran
calls required for computation of many probabilities.

### Value

Numeric vector of probabilities.

### Author(s)

Fortran code by Alan Genz (see references). R interface by Brenton Kenkel ([email protected]), based on code from Adelchi Azzalini's mnormt package.

### References

Genz, A. (1992). Numerical Computation of Multivariate Normal
Probabilities. *J. Computational and Graphical Statist.*, **1**,
141–149.

Genz, A. (1993). Comparison of methods for the computation of multivariate
normal probabilities. *Computing Science and Statistics*, **25**,
400–405.

Genz, A. Fortran code for `MVTDSTPACK`

available at
http://www.math.wsu.edu/math/faculty/genz/software/fort77/mvtdstpack.f
(as of 2011-02-21).

### Examples

```
x <- rnorm(10)
y <- rnorm(10)
rho <- runif(10)
pbivnorm(x, y, rho)
X <- cbind(x, y)
pbivnorm(X, rho = rho)
## rho can be a single value, unless recycling is disallowed
rho <- runif(1)
pbivnorm(x, y, rho)
```