Abstract
The Wishart distribution and its generalizations are among the most prominent
probability distributions in multivariate statistical analysis, arising
naturally in applied research and as a basis for theoretical models. In this
paper, we generalize the Wishart distribution utilizing a different approach
that leads to the Wishart generator distribution with the Wishart distribution
as a special case. It is not restricted, however some special cases are
exhibited. Important statistical characteristics of the Wishart generator
distribution are derived from the matrix theory viewpoint. Estimation is also
touched upon as a guide for further research from the classical approach as
well as from the Bayesian paradigm. The paper is concluded by giving
applications of two special cases of this distribution in calculating the
product of beta functions and astronomy.
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