# Conditional Multivariate Normal Distribution

### Description

Computes the distribution function of the conditional multivariate normal, [Y given X], where Z = (X,Y) is the fully-joint multivariate normal distribution with mean equal to `mean`

and covariance matrix `sigma`

.

### Usage

1 2 3 |

### Arguments

`lower` |
the vector of lower limits of length n. |

`upper` |
the vector of upper limits of length n. |

`mean` |
the mean vector of length n. |

`sigma` |
a symmetric, positive-definte matrix, of dimension n x n, which must be specified. |

`dependent.ind` |
a vector of integers denoting the indices of the dependent variable Y. |

`given.ind` |
a vector of integers denoting the indices of the conditioning variable X. |

`X.given` |
a vector of reals denoting the conditioning value of X. When both |

`check.sigma` |
logical; if |

`algorithm` |
an object of class |

`...` |
additional parameters (currently given to |

### Details

This program involves the computation of multivariate normal probabilities with arbitrary correlation matrices.

### Value

The evaluated distribution function is returned with attributes

`error` |
estimated absolute error and |

`msg` |
status messages. |

### See Also

`dcmvnorm`

, `rcmvnorm`

, `pmvnorm`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
n <- 10
A <- matrix(rnorm(n^2), n, n)
A <- A %*% t(A)
pcmvnorm(lower=-Inf, upper=1, mean=rep(1,n), sigma=A, dependent.ind=3, given.ind=c(1,4,7,9,10),
X.given=c(1,1,0,0,-1))
pcmvnorm(lower=-Inf, upper=c(1,2), mean=rep(1,n),
sigma=A, dep=c(2,5), given=c(1,4,7,9,10),
X=c(1,1,0,0,-1))
pcmvnorm(lower=-Inf, upper=c(1,2), mean=rep(1,n), sigma=A,
dep=c(2,5))
``` |

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