pcmvnorm {condMVNorm} R Documentation

## 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

pcmvnorm(lower=-Inf, upper=Inf, mean, sigma,
dependent.ind, given.ind, X.given,
check.sigma=TRUE, algorithm = GenzBretz(), ...)


### 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. If specified as integer vector of length zero or left unspecified, the unconditional distribution is used. X.given a vector of reals denoting the conditioning value of X. This should be of the same length as given.ind check.sigma logical; if TRUE, the variance-covariance matrix is checked for appropriateness (symmetry, positive-definiteness). This could be set to FALSE if the user knows it is appropriate. algorithm an object of class GenzBretz, Miwa or TVPACK specifying both the algorithm to be used as well as the associated hyper parameters. ... additional parameters (currently given to GenzBretz for backward compatibility issues).

### 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.

dcmvnorm, rcmvnorm, pmvnorm.

### Examples

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))



[Package condMVNorm version 2020.1 Index]