Calculations involving the multivariate normal and multivariate t distributions with and without truncation

TL;DR

This paper introduces Stata commands and Mata functions for efficiently computing densities, distribution functions, quantiles, and pseudo-random vectors of multivariate normal and non-central multivariate t distributions, including truncated cases.

Contribution

It provides new computational tools for evaluating multivariate distributions with and without truncation within the Stata environment.

Findings

Efficient computation of distributional quantities

Support for truncated multivariate distributions

Implementation in Stata and Mata

Abstract

This paper presents a set of Stata commands and Mata functions to evaluate different distributional quantities of the multivariate normal distribution, and a particular type of non-central multivariate t distribution. Specifically, their densities, distribution functions, equicoordinate quantiles, and pseudo-random vectors can be computed efficiently, either in the absence or presence of variable truncation.