mtmvnorm {tmvtnorm} | R Documentation |
Computation of the first two moments, i.e. mean vector and covariance matrix for the Truncated Multivariate Normal Distribution based on the works of Tallis (1961), Lee (1979) and Leppard and Tallis (1989), but extended to the double-truncated case with general mean and general covariance matrix.
mtmvnorm(mean, sigma, lower, upper)
mean |
Mean vector, default is rep(0, length = ncol(x)) . |
sigma |
Covariance matrix, default is diag(ncol(x)) . |
lower |
Vector of lower truncation points,\
default is rep(-Inf, length = length(mean)) . |
upper |
Vector of upper truncation points,\
default is rep( Inf, length = length(mean)) . |
mean |
Mean vector of truncated variables |
cov |
Covariance matrix of truncated variables |
Stefan Wilhelm <Stefan.Wilhelm@financial.com>, Manjunath B G <bgmanjunath@gmail.com>
Tallis, G. M. (1961). The moment generating function of the truncated multinormal distribution. Journal of the Royal Statistical Society, Series B, 23, 223–229
Lee, L.-F. (1979). On the first and second moments of the truncated multi-normal distribution and a simple estimator. Economics Letters, 3, 165–169
Leppard, P. and Tallis, G. M. (1989). Evaluation of the Mean and Covariance of the Truncated Multinormal. Applied Statistics, 38, 543–553
Manjunath B G and Wilhelm, S. (2009). Moments Calculation For the Double Truncated Multivariate Normal Density. Working Paper. Available at SSRN: http://ssrn.com/abstract=1472153
mu <- c(0.5, 0.5, 0.5) sigma <- matrix(c( 1, 0.6, 0.3, 0.6, 1, 0.2, 0.3, 0.2, 2), 3, 3) a <- c(-Inf, -Inf, -Inf) b <- c(1, 1, 1) # compute first and second moments mtmvnorm(mu, sigma, lower=a, upper=b) # compare with simulated results X <- rtmvnorm(n=1000, mean=mu, sigma=sigma, lower=a, upper=b) colMeans(X) cov(X)