# Truncated Multivariate Normal 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 |

### 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 |

`lower` |
Vector of lower truncation points,\
default is |

`upper` |
Vector of upper truncation points,\
default is |

`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 |