Many methods exist in the literature for testing multivariate normality. They can be grouped into graphical and numerical methods. While it is known that the multivariate t-distribution is more realistic for modelling empirical data than the multivariate normal distribution due to its heavier tail, unfortunately there are only a few of goodness-of-fit tests for the multivariate t-distribution. One example is based on the Rényi entropy of order λ, which can be used in comparing the shape, densities, and measuring the heaviness of tails of the distributions. However, the application of this method is a bit complicated and time-consuming. Another method is based on Skewness and Kurtosis; it uses Monte Carlo Simulation for multivariate t-distribution testing. Hypothesis testing with Monte Carlo simulation is considered to have advantages over other classical hypothesis testing statistics because it is simpler and faster to compute. For multivariate t-distribution testing, the latter method is easier to understand, simpler, and easier to apply than earlier methods. Implementing this method in MATLAB would still require some MATLAB toolbox functions. On the other hand, the statistical environment R is an open source software package and a powerful tool for statistical data analysis and graphical representation. R provides the opportunity for many individuals to improve its code and add functions. This study aims to illustrate the procedure of a goodness-of-fit test of the multivariate t-distribution with Monte Carlo simulation using R as an open source alternative to MATLAB. Based on the p-values of the Skewness and Kurtosis tests (both univariate and multivariate) on the generated multivariate t-distribution data, it is shown that the simulation data can more accurately be assumed to follow a multivariate t-distribution. It is expected that this study can be beneficial for other researchers who want to do goodness-of-fit tests of a multivariate t-distribution.

1.
R.
Kan
and
G.
Zhou
,
Modeling Non-normality Using Multivariate t: Implications for Asset Pricing
,
2006
. (Accessed from http://apps.olin.wustl.edu/faculty/zhou/KZ-t-06.pdf.).
2.
A.
Batsidis
and
K.
Zografos
,
J. Multivar. Anal.
113
,
91
105
(
2013
).
3.
K. S.
Song
,
J. Stat. Plan. Infer.
(
2001
).
4.
K.
Zografos
,
J. Multivar. Anal.
99
,
858
879
(
2008
).
5.
S.
Kotz
and
S.
,
Multivariate t Distributions and Their Applications
. (
Cambridge University Press
,
Cambridge, United Kingdom
,
2004
.)
6.
P.
Natalya
,
V.
Vassilly
,
M.
Rashid
and
V.
Yevgeniy
,
Goodness of Fit Tests for Multivariate Normality
,
2016
. (Accessed from https://cran.r-project.org/web/packages/mvnTest/mvnTest.pdf).
7.
K. V.
Mardia
,
Biometrika
,
57
,
519
530
(
1970
).
8.
J. O.
Ramsay
,
G.
Hooker
and
S.
Graves
,
Functional Data Analysis with R and MATLAB
. (
New York
,
Springer
,
2009
).
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