tmvtnorm (version 0.8-3)

ptmvnorm: 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 s

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.

Value

• The evaluated distribution function is returned with attributes
• error
  estimated absolute error and
• msg
  status messages.

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).

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