Moments Calculation For the Doubly Truncated Multivariate Normal Density

Understand

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.