Weighted-Type Wishart Distributions with Application

Abstract

In this paper, we consider a general framework for constructing new valid densities regarding a random matrix variate. However, we focus specifically on the Wishart distribution. The methodology involves coupling the density function of the Wishart distribution with a Borel measurable function as a weight. We propose three different weights by considering trace and determinant operators on matrices. The characteristics for the proposed weighted-type Wishart distributions are studied and the enrichment of this approach is illustrated. A special case of this weighted-type distribution is applied in the Bayesian analysis of the normal model in the univariate and multivariate cases. It is shown that the performance of this new prior model is competitive using various measures.

Keywords

• Bayesian analysis
• eigenvalues
• Kummer gamma
• Kummer Wishart
• matrix variate
• weight function