Generate random numbers from the multivariate normal distribution
rmnorm generate random numbers from a multivariate normal distribution.
the number of random vectors to be generated.
a vector with means of length d.
a variance-covariance matrix with dimentions d * d.
This is a modification of the function
rmnorm provided in mnormt.
The function works around problems of non-positive definite
variance-covariance matrices due to numerical rounding by use of the
nearPD. Furthermore, when only a single random vector
is generated, the function now returns a named random vector with names
inherited from the colum names of the variance-covariance matrix.
For n > 1
rmnorm returns a matrix of
n rows of random vectors,
while for n = 1
rmnorm returns a named random vector.
Fortran code of SADMVN and most auxiliary functions by Alan Genz, some additional auxiliary functions by people referred to within his program. Porting to R and additional R code by Adelchi Azzalini, with current modifications by Thomas Kvalnes.
Genz, A. 1992. Numerical Computation of Multivariate Normal Probabilities. Journal of Computational and Graphical Statiststics, 1, 141-149.
Genz, A. 1993. Comparison of methods for the computation of multivariate normal probabilities. Computing Science and Statistics, 25, 400-405.
Genz, A.: Fortran code available at http://www.math.wsu.edu/math/faculty/genz/software/fort77/mvn.f
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#Variance-covariance matrix varcov <- matrix(c(2.047737e-03, 3.540039e-05, 0.0075178920, 3.540039e-05, 6.122832e-07, 0.0001299661, 7.517892e-03, 1.299661e-04, 0.0276005740), ncol = 3) #Set names nam <- c("a", "b", "c") dimnames(varcov) <- list(nam, nam) #Check positive definiteness (all positive eigenvalues = positive definite) eigen(varcov) $values #Mean mean <- c(1, 0.3, 0.5) #Generate n = 1 random vector rmnorm(n = 1, mean = mean, varcov = varcov) #Generate n = 10 random vectors rmnorm(n = 10, mean = mean, varcov = varcov) #Generate n = 1 random vectors when varcov is non-positive definite #Non-positive definite varcov matrix varcov2 <- matrix(c(2.04e-03, 3.54e-05, 7.52e-03, 3.54e-05, 6.15e-07, 1.30e-04, 7.52e-03, 1.30e-04, 2.76e-02), ncol = 3) dimnames(varcov2) <- dimnames(varcov) eigen(varcov2) #Random vector rmnorm(n = 1, mean = mean, varcov = varcov2)
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