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