1d:T7ef,# Random number generation for truncated multivariate normal distribution subject to linear inequality constraints `rtmvn` simulates truncated multivariate (p-dimensional) normal distribution subject to linear inequality constraints. The constraints should be written as a matrix (`D`) with `lower` and `upper` as the lower and upper bounds for those constraints respectively. Note that `D` can be non-full rank, which generalize many traditional methods. ```r rtmvn( n, Mean, Sigma, D = diag(1, length(Mean)), lower, upper, int = NULL, burn = 10, thin = 1 ) ``` ## Arguments - `n`: number of random samples desired (sample size). - `Mean`: mean vector of the underlying multivariate normal distribution. - `Sigma`: positive definite covariance matrix of the underlying multivariate normal distribution. - `D`: matrix or vector of coefficients of linear inequality constraints. - `lower`: vector of lower bounds for truncation. - `upper`: vector of upper bounds for truncation. - `int`: initial value vector for Gibbs sampler (satisfying truncation), if `NULL` then determine automatically. - `burn`: burn-in iterations discarded (default as `10`). - `thin`: thinning lag (default as `1`). ## Returns `rtmvn` returns a (`n*p`) matrix (or vector when `n=1`) containing random numbers which approximately follows truncated multivariate normal distribution. ## Examples ```r # Example for full rank with strong dependence d <- 3 rho <- 0.9 Sigma <- matrix(0, nrow=d, ncol=d) Sigma <- rho^abs(row(Sigma) - col(Sigma)) D1 <- diag(1,d) # Full rank set.seed(1203) ans.1 <- rtmvn(n=1000, Mean=1:d, Sigma, D=D1, lower=rep(-1,d), upper=rep(1,d), int=rep(0,d), burn=50) apply(ans.1, 2, summary) # Example for non-full rank d <- 3 rho <- 0.5 Sigma <- matrix(0, nrow=d, ncol=d) Sigma <- rho^abs(row(Sigma) - col(Sigma)) D2 <- matrix(c(1,1,1,0,1,0,1,0,1),ncol=d) qr(D2)$rank # 2 set.seed(1228) ans.2 <- rtmvn(n=100, Mean=1:d, Sigma, D=D2, lower=rep(-1,d), upper=rep(1,d), burn=10) apply(ans.2, 2, summary) ```

rtmvn function