mtmvnorm {tmvtnorm}R Documentation

Computation of Mean Vector and Covariance Matrix For Truncated Multivariate Normal Distribution

Description

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.

Usage

mtmvnorm(mean, sigma, lower, upper)

Arguments

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)).

Value

mean Mean vector of truncated variables
cov Covariance matrix of truncated variables

Author(s)

Stefan Wilhelm <Stefan.Wilhelm@financial.com>, Manjunath B G <bgmanjunath@gmail.com>

References

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

Examples

  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)

[Package tmvtnorm version 0.8-3 Index]