fastmatrix (version 0.5-7721)

rmnorm: Multivariate normal random deviates

Description

Random number generation from the multivariate normal (Gaussian) distribution.

Usage

rmnorm(n = 1, mean = rep(0, nrow(Sigma)), Sigma = diag(length(mean)))

Value

If \(n = 1\) a vector of the same length as mean, otherwise a matrix of \(n\) rows of random vectors.

Arguments

n

the number of samples requested

mean

a vector giving the means of each variable

Sigma

a positive-definite covariance matrix

Details

The function rmnorm is an interface to C routines, which make calls to subroutines from LAPACK. The matrix decomposition is internally done using the Cholesky decomposition. If Sigma is not non-negative definite then there will be a warning message.

References

Devroye, L. (1986). Non-Uniform Random Variate Generation. Springer-Verlag, New York.

See Also

rnorm

Examples

# covariance parameters
Sigma <- matrix(c(10,3,3,2), ncol = 2)
Sigma

# generate the sample
y <- rmnorm(n = 1000, Sigma = Sigma)
var(y)

# scatterplot of a random bivariate normal sample with mean
# vector zero and covariance matrix 'Sigma'
par(pty = "s")
plot(y, xlab = "", ylab = "")
title("bivariate normal sample", font.main = 1)

# QQ-plot of transformed distances
z <- WH.normal(y)
par(pty = "s")
qqnorm(z, main = "Transformed distances QQ-plot")
abline(c(0,1), col = "red", lwd = 2, lty = 2)