ptmvnorm {tmvtnorm}R Documentation

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

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).

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

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


[Package tmvtnorm version 0.4-2 Index]