# trmvrnorm_rej_cpp: Sample from truncated multivariate normal distribution with... In anMC: Compute High Dimensional Orthant Probabilities

 trmvrnorm_rej_cpp R Documentation

## Sample from truncated multivariate normal distribution with C++

### Description

Simulates realizations from a truncated multivariate normal with mean mu, covariance matrix sigma in the bounds lower upper.

### Usage

``````trmvrnorm_rej_cpp(n, mu, sigma, lower, upper, verb)
``````

### Arguments

 `n` number of simulations. `mu` mean vector. `sigma` covariance matrix. `lower` vector of lower bounds. `upper` vector of upper bounds. `verb` level of verbosity: if lower than 3 nothing, 3 minimal, 4 extended.

### Value

A matrix of size `d x n` containing the samples.

### References

Horrace, W. C. (2005). Some results on the multivariate truncated normal distribution. Journal of Multivariate Analysis, 94(1):209–221.

Robert, C. P. (1995). Simulation of truncated normal variables. Statistics and Computing, 5(2):121–125.

### Examples

``````# Simulate 1000 realizations from a truncated multivariate normal vector
mu <- rep(0,10)
Sigma <- diag(rep(1,10))
upper <- rep(3,10)
lower <- rep(-0.5,10)
realizations<-trmvrnorm_rej_cpp(n=1000,mu = mu,sigma=Sigma, lower =lower, upper= upper,verb=3)
empMean<-rowMeans(realizations)
empCov<-cov(t(realizations))
# check if the sample mean is close to the actual mean
maxErrorOnMean<-max(abs(mu-empMean))
# check if we can estimate correctly the covariance matrix
maxErrorOnVar<-max(abs(rep(1,200)-diag(empCov)))
maxErrorOnCov<-max(abs(empCov[lower.tri(empCov)]))
## Not run:
plot(density(realizations[1,]))
hist(realizations[1,],breaks="FD")

## End(Not run)
``````

anMC documentation built on Aug. 22, 2023, 5:08 p.m.