In this article, we present a set of commands and Mata functions to evaluate different distributional quantities of the multivariate normal distribution and a particular type of noncentral multivariate t distribution. Specifically, their densities, distribution functions, equicoordinate quantiles, and pseudo–random vectors can be computed efficiently, in either the absence or the presence of variable truncation.
BlæsildP., and GranfeldtJ.2002. Statistics with Applications in Biology and Geology.Boca Raton, FL: Chapman & Hall/CRC.
2.
CappellariL., and JenkinsS. P.2006. Calculation of multivariate normal probabilities by simulation, with applications to maximum simulated likelihood estimation. Stata Journal6: 156–189.
3.
FeigelsonE. D., and BabuG. J.2012. Modern Statistical Methods for Astronomy: With R Applications.Cambridge: Cambridge University Press.
4.
GatesR.2006. A Mata Geweke–Hajivassiliou–Keane multivariate normal simulator. Stata Journal6: 190–213.
5.
GenzA.1992. Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics1: 141–149.
6.
GenzA., and BretzF.2002. Comparison of methods for the computation of multivariate t probabilities. Journal of Computational and Graphical Statistics11: 950–971.
7.
GenzA., and BretzF.2009. Computation of Multivariate Normal and t Probabilities.Berlin: Springer.
8.
GenzA., BretzF., MiwaT., MiX., LeischF., ScheiplF., BornkampB., MaechlerM., and HothornT.2018. mvtnorm: Multivariate normal and t distributions. R package version 1.0-8. https://cran.r-project.org/web/packages/mvtnorm/.
9.
GewekeJ.1989. Bayesian inference in econometric models using Monte Carlo integration. Econometrica57: 1317–1339.
10.
GibsonG. J., GlasbeyC. A., and ElstonD. A.1994. Monte Carlo evaluation of multi-variate normal integrals and sensitivity to variate ordering. In Advances in Numerical Methods and Applications: Proceedings of the Third International Conference, ed. DimovI. T., SendovB., and VassilevskiP. S., 120–126. River Edge, NJ: World Scientific.
11.
HajivassiliouV. A., and McFaddenD. L.1998. The method of simulated scores for the estimation of LDV models. Econometrica66: 863–896.
12.
HowellD. C.2012. Statistical Methods for Psychology.8th ed.Belmont, CA: Wadsworth.
13.
IrelandC. R.2010. Experimental Statistics for Agriculture and Horticulture.Wallingford, UK: CABI.
14.
JohnsonM. E.1987. Multivariate Statistical Simulation: A Guide to Selecting and Generating Continuous Multivariate Distributions.Chichester, UK: Wiley.
15.
KeaneM. P.1994. A computationally practical simulation estimator for panel data. Econometrica62: 95–116.
16.
KotzS., BalakrishnanN., and JohnsonN. L.2004. Continuous Multivariate Distributions. Volume 1: Models and Applications.2nd ed.New York: Wiley.
17.
KotzS., and NadarajahS.2004. Multivariate t Distributions and Their Applications.Cambridge: Cambridge University Press.
18.
MazzaC., and BenaïmM.2014. Stochastic Dynamics for Systems Biology.Boca Raton, FL: Chapman & Hall/CRC.
19.
PatelJ. K., and ReadC. B.1996. Handbook of the Normal Distribution.Revised and expanded second ed. New York: Marcel Dekker.
20.
PiegorschW. W., and BailerA. J.1997. Statistics for Environmental Biology and Toxicology.London: Chapman & Hall/CRC.
21.
StevensJ. P.2016. Applied Multivariate Statistics for the Social Sciences: Analyses with SAS and IBMs SPSS.6th ed.New York: Routledge.
22.
TobinJ.1958. Estimation of relationships for limited dependent variables. Econometrica26: 24–36.
23.
TongY. L.1990. The Multivariate Normal Distribution.New York: Springer.
