generator of independent and identically distributed random vectors from the truncated univariate and multivariate distributions;
(Quasi-) Monte Carlo estimator and a deterministic upper bound of the cumulative distribution function of the multivariate normal;
algorithm for the accurate computation of the quantile function of the normal distribution in the extremes of its tails.
Details
Package:
Truncated Normal
Type:
Package
Version:
1.0
Date:
2015-11-08
License:
GPL-3
mvNcdf(l,u,Sig,n)
uses a Monte Carlo sample of size n to estimate the cumulative
distribution function, Pr( l < X < u), of the d-dimensional
multivariate normal with zero-mean and covariance Σ, that is,
X has N(0,Σ) distribution;
mvNqmc(l,u,Sig,n)
provides a Quasi Monte Carlo algorithm for medium dimensions
(say, d<50), in addition to the faster Monte Carlo algorithm in mvNcdf;
mvrandn(l,u,Sig,n)
simulates nidentically and independently distributed random vectors X from N(0,Σ), conditional on l<X<u;
norminvp(p,l,u)
computes the quantile function at 0≤ p≤ 1 of the univariate N(0,1) distribution
truncated to [l,u], and with high precision in the tails;
trandn(l,u)
is a fast random number generator from the univariate N(0,1)
distribution truncated to [l,u].
Z. I. Botev (2015), The Normal Law Under Linear Restrictions:
Simulation and Estimation via Minimax Tilting, submitted to JRSS(B)
Z. I. Botev and P. L'Ecuyer (2015), Efficient Estimation
and Simulation of the Truncated Multivariate Student-t Distribution, Proceedings of the 2015 Winter Simulation Conference,
Huntington Beach, CA, USA
Gibson G. J., Glasbey C. A., Elston D. A. (1994),
Monte Carlo evaluation of multivariate normal integrals and sensitivity to variate ordering,
In: Advances in Numerical Methods and Applications, pages 120–126
providing 
.