# ptmvnorm: Truncated Multivariate Normal Distribution In tmvtnorm: Truncated Multivariate Normal and Student t Distribution

## Description

Computes the distribution function of the truncated multivariate normal distribution for arbitrary limits and correlation matrices based on the `pmvnorm()` implementation of the algorithms by Genz and Bretz.

## Usage

 ```1 2 3 4``` ```ptmvnorm(lowerx, upperx, mean=rep(0, length(lowerx)), sigma, lower = rep(-Inf, length = length(mean)), upper = rep( Inf, length = length(mean)), maxpts = 25000, abseps = 0.001, releps = 0) ```

## Arguments

 `lowerx` the vector of lower limits of length n. `upperx` the vector of upper limits of length n. `mean` the mean vector of length n. `sigma` the covariance matrix of dimension n. Either `corr` or `sigma` can be specified. If `sigma` is given, the problem is standardized. If neither `corr` nor `sigma` is given, the identity matrix is used for `sigma`. `lower` Vector of lower truncation points,\ default is `rep(-Inf, length = length(mean))`. `upper` Vector of upper truncation points,\ default is `rep( Inf, length = length(mean))`. `maxpts` maximum number of function values as integer. `abseps` absolute error tolerance as double. `releps` relative error tolerance as double.

## Details

The computation of truncated multivariate normal probabilities and densities is done using conditional probabilities from the standard/untruncated multivariate normal distribution. So we refer to the documentation of the `mvtnorm` package and the methodology is described in Genz (1992, 1993) and Genz/Bretz (2009).

For properties of the truncated multivariate normal distribution see for example Johnson/Kotz (1970) and Horrace (2005).

## Value

The evaluated distribution function is returned with attributes

 `error` estimated absolute error and `msg` status messages.

## References

Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1, 141–150

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

Genz, A. and Bretz, F. (2009). Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195, Springer-Verlag, Heidelberg.

Johnson, N./Kotz, S. (1970). Distributions in Statistics: Continuous Multivariate Distributions Wiley & Sons, pp. 70–73

Horrace, W. (2005). Some Results on the Multivariate Truncated Normal Distribution. Journal of Multivariate Analysis, 94, 209–221

## Examples

 ```1 2 3``` ``` sigma <- matrix(c(5, 0.8, 0.8, 1), 2, 2) Fx <- ptmvnorm(lowerx=c(-1,-1), upperx=c(0.5,0), mean=c(0,0), sigma=sigma, lower=c(-1,-1), upper=c(1,1)) ```

### Example output

```Loading required package: mvtnorm