The multivariate truncated normal distribution
The probability density function, the distribution function and random number generation for the multivariate truncated normal (Gaussian) distribution
dmtruncnorm(x, mean, varcov, lower, upper, log = FALSE, ...) pmtruncnorm(x, mean, varcov, lower, upper, ...) rmtruncnorm(n, mean, varcov, lower, upper)
x |
either a vector of length |
mean |
a vector representing the mean value of the pre-truncation normal distribution. |
varcov |
a symmetric positive-definite matrix representing the variance matrix of the pre-truncation normal distribution. |
lower |
a vector representing the lower truncation values of the
component variables; |
upper |
a vector representing the upper truncation values of the
component variables; |
log |
a logical value (default value is |
... |
arguments passed to |
n |
the number of (pseudo) random vectors to be generated. |
For dmtruncnorm and pmtruncnorm,
the dimension d cannot exceed 20.
Function rmtruncnorm is just a wrapper of the imported function
tmvnsim, set up so that the names and the pattern of
the rmtruncnorm arguments are in agreement with the other functions
in the package.
a numeric vector in case of dmtruncnorm and pmtruncnorm;
a matrix in case of rmtruncnorm, unless n=1 in which case
it is a vector.
Adelchi Azzalini
m2 <- c(0.5, -1) V2 <- matrix(c(3, 3, 3, 6), 2, 2) lower <- a <- c(-1, -2.5) upper <- b <- c(2, 1) set.seed(1) # generate a set of coordinates, pts, on the plane pts <- matrix(runif(10, min=-1.5, max=1.5), nrow=5, ncol=2) rownames(pts) <- LETTERS[1:nrow(pts)] # compute PDF and CDF at the chosen coordinates, pts pdf <- dmtruncnorm(pts, mean=m2, varcov=V2, lower, upper) cdf <- pmtruncnorm(pts, mean=m2, varcov=V2, lower, upper) print(cbind(pts, pdf, cdf)) #-- # generate a sample of random numbers sample <- rmtruncnorm(300, mean=m2, varcov=V2, lower, upper) # # then plot the sample along with the pertaining box and the earlier points, # just for graphical illustration eps <- 0.5 ra <- lower -eps rb <- upper + eps plot(x=c(ra[1], rb[1]), y=c(ra[2], rb[2]), xlab="", ylab="",type="n") points(sample, pch=20, col=4, cex=0.4) xbox <- c(a[1], b[1], b[1], a[1], a[1]) ybox <- c(a[2], a[2], b[2], b[2], a[2]) polygon(xbox, ybox, lty=2, border="gray60") text(pts[,1], pts[,2], col=2, labels=rownames(pts), cex=0.9)
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