A pathway to matrix-variate gamma and normal densities

By Arak M. Mathai. 2005

186 citations recorded by the source corpus.

A general real matrix-variate probability model is introduced here, which covers almost all real matrix-variate densities used in multivariate statistical analysis. Through the new density introduced here, a pathway is created to go from matrix-variate type-1 beta to matrix-variate type-2 beta to matrix-variate gamma to matrix-variate Gaussian or normal densities. Other densities such as extended matrix-variate Student t, F, Cauchy density will also come in as particular cases. Connections to the distributions of quadratic forms and generalized quadratic forms in the new matrix are established. The present day analysis of these problems is mainly confined to Gaussian random variables. Thus, through the new distribution, all these theories are extended. Connections to certain geometrical probability problems, such as the distribution of the volume of a random parallelotope in Euclidean space, is also established.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a2cb393ec32d699dc5c0ceb15f944a6e7b66ca50

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Citations in the corpus

PATHWAY FRACTIONAL INTEGRATION OPERATOR (2009, methodology): “[15] A.M. Mathai and H. J. Haubold, Pathway model, superstatistics, Tsallis statistics and a generalized measure of entropy.”
Simple Marginally Noninformative Prior Distributions for Covariance Matrices (2013, methodology): “from which it can be seen that the proposed family appears implicitly in Mathai (2005). In that paper, an explicit density representation is given for a more general class of matrix distributions and some theoretical properties are derived, but no feasible method to fit such models to data is prescr”
Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy (2006, methodology): “When α → 1 both (38) and (41) will approach the generalized gamma form Equations (38) , (41) and (42) are special scalar cases of the pathway model of Mathai (2005).”