package contains a set of routines to
perform estimation and inference under the multivariate t-distribution. These methods are
a direct generalization of the multivariate inference under the gaussian assumption. In
addition, these procedures provide robust methods useful against outliers. The package uses
these functions in algorithms to simulate, analyze, and fit the model to data. The methodology
is described, with examples, in the following paper.
**MVT**

- Basic functionality for modeling using the multivariate t-distribution.
- Estimation of mean, covariance matrix and the shape (kurtosis) parameter using the EM algorithm.
- The core routines have been implemented in C and linked to R to ensure a reasonable computational speed.
- Performs hypothesis testing about the equicorrelation or homogeneity of variances structures for the covariance matrix, considering the test statistics of likelihood ratio, score, Wald or gradient.
- Multivariate random number generation for the multivariate t- (and gaussian) distribution.
- Graphical methods for assessing the assumption of multivariate t- (and gaussian) distribution.

Please report any bugs/suggestions/improvements to Felipe Osorio, Universidad Técnica Federico Santa María. If you find these routines useful or not then please let me know. Also, acknowledgement of the use of the routines is appreciated.

Latest binaries and sources for MVT are available from CRAN package repository .

- MVT_0.3-8.tar.gz - Package sources
- MVT_0.3-8.zip - Windows binaries (R-release)
- MVT_0.3-8.tgz - MacOS binaries (R-release, arm64)
- MVT_0.3-8.tgz - MacOS binaries (R-release, x86_64)
- MVT.pdf - Reference Manual

To install this package, start R and enter:

Alternatively, you can download the source as a tarball or as a zip file. Unpack the tarball or zipfile (thereby creating a directory named, MVT) and install the package source by executing (at the console prompt)

Next, you can load the package by using the command: `library(MVT)`

Osorio, F. (2023). *Estimation and testing for the multivariate t-distribution*.
R package version 0.3-8, http://mvt.mat.utfsm.cl.

Osorio, F., Galea, M., Henríquez, C., Arellano-Valle, R. (2023). Addressing non-normality in multivariate analysis using the t-distribution. AStA Advances in Statistical Analysis , doi: 10.1007/s10182-022-00468-2.

- Mignemi, G., Panzeri, A., Granziol, U., Bruno, G., Bertamini, M., Vidotto, G., Spoto, A. (2022). The mediating role of scientifical-medical satisfaction between COVID-19 conspiracy beliefs and vaccine confidence: A two-waves structural equation model. Journal of Behavioral Medicine , doi: 10.1007/s10865-022-00322-5.
- Hintz, E., Hofert, M., Lemieux, C. (2022). Multivariate Normal Variance Mixtures in R: The R Package nvmix. Journal of Statistical Software 102, 1-31.
- Punzo, A., Bagnato, L. (2020). Allometric analysis using the multivariate shifted exponential normal distribution. Biometrical Journal 62, 1525-1543.

I'm Assistant Professor at Department of Mathematics of the Universidad Técnica Federico Santa María, Chile.

- Webpage: fosorios.mat.utfsm.cl
- Email: felipe.osorios@usm.cl

I contribute as developer/maintainer of the following R packages:

- fastmatrix - Fast computation of some matrices useful in statistics.
- HEAVY - Robust estimation using heavy-tailed distributions.
- L1pack - Routines for L1 estimation.
- SpatialPack - Package for analysis of spatial data.