Moments Calculation For the Doubly Truncated Multivariate Normal Density
Abstract
In the present article we derive an explicit expression for the trun- cated mean and variance for the multivariate normal distribution with ar- bitrary rectangular double truncation. We use the moment generating ap- proach of Tallis (1961) and extend it to general {\mu}, {\Sigma} and all combinations of truncation. As part of the solution we also give a formula for the bivari- ate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after trunca- tion. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.
Cite
@article{arxiv.1206.5387,
title = {Moments Calculation For the Doubly Truncated Multivariate Normal Density},
author = {Manjunath B G and Stefan Wilhelm},
journal= {arXiv preprint arXiv:1206.5387},
year = {2012}
}