pmvnorm {mvtnorm} | R Documentation |
Computes the distribution function of the multivariate normal distribution for arbitrary limits and correlation matrices based on algorithms by Genz and Bretz.
pmvnorm(mean, corr, lower, upper, maxpts = 25000, abseps =0.001, releps = 0)
mean |
the mean vector of length n. |
corr |
the correlation matrix of dimension n. |
lower |
the vector of lower limits of length n. |
upper |
the vector of upper limits of length n. |
maxpts |
maximum number of function values as integer. |
abseps |
absolute error tolerance as double. |
releps |
relative error tolerance as double. |
This program involves the computation of multivariate normal-probabilities with arbitrary correlation matrices. It involves both the computation of singular and nonsingular probabilities. The methodology is described in Genz (1992, 1993).
Note that both -Inf
and +Inf
may be specified in lower
and
upper
. For more details see pmvt
.
The mvn case is treated as a special case of pmvt
with df=0
.
Univariate problems are passed to pnorm
.
Multivariate normal density and random numbers are available using
dmvnorm
and mvrnorm
.
A list with the following components:
value |
estimated integral value. |
error |
estimated absolute error. |
msg |
status messages. |
Fortran Code by Alan Genz <AlanGenz@wsu.edu> and Frank Bretz <bretz@ifgb.uni-hannover.de>, R port by Torsten Hothorn <Torsten.Hothorn@rzmail.uni-erlangen.de>
Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1, 141150
Genz, A. (1993). Comparison of methods for the computation of multivariate normal probabilities. Computing Science and Statistics, 25, 400405
n <- 5 mean <- rep(0, 5) lower <- rep(-1, 5) upper <- rep(3, 5) corr <- diag(5) corr[lower.tri(corr)] <- 0.5 prob <- pmvnorm(mean, corr, lower, upper) print(prob) pmvnorm(0, 1, -Inf, 3)$value == pnorm(3)