Wishart Generator Distribution

TL;DR

This paper introduces the Wishart generator distribution, a new generalization of the Wishart distribution, with derived properties, estimation methods, and applications in statistics and astronomy.

Contribution

It proposes a novel generalization of the Wishart distribution, expanding its theoretical framework and practical applications.

Findings

Derived statistical characteristics of the Wishart generator distribution.

Provided estimation approaches from classical and Bayesian perspectives.

Illustrated applications in calculating beta functions and astronomy.

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.