This research paper stands for an extension to the multivariate
t?distribution introduced in 1954 by Cornish, Dunnett and Sobel, namely the
multiparameter t?distribution. This distribution is expressed in two
different ways. The first way invests the mixture of a normal vector with a
natural extension to the Wishart distribution, that is the Riesz
distribution on symmetric matrices. The second one rests upon the Cholesky
decomposition of the Riesz matrix. An algorithm for generating this
distribution is investigated using the Riesz distribution arising obtained
through not only the distribution of the empirical normal covariance matrix
for samples with monotone missing data but also through Cholesky
decomposition. In addition, Some fundamentals properties of the
multiparameter t?distribution such as the infinite divisibility are
identified. Besides, the Expectation Maximization algorithm is used to
estimate its parameters. Finally, the performance of these estimators is
assessed by means of the Mean Squared Error between the true and the
estimated parameters.