The multiparameter t’distribution

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.

Riesz and beta-Riesz distributions

This article derives several properties of the Riesz distributions, such as their corresponding Bartlett decompositions, the inverse Riesz distributions and the distribution of the generalised variance for real normed division algebras. In addition, introduce a kind of generalised beta distribution termed beta-Riesz distribution for real normed division algebras. Two versions of this distributions are proposed and some properties are studied.