In this paper, we consider a general framework for constructing new valid densitiesregarding a random matrix variate. However, we focus specifically on the Wishartdistribution. The methodology involves coupling the density function of the Wishartdistribution with a Borel measurable function as a weight. We propose three differentweights by considering trace and determinant operators on matrices. The charac-teristics for the proposed weighted-type Wishart distributions are studied and theenrichment of this approach is illustrated. A special case of this weighted-type dis-tribution is applied in the Bayesian analysis of the normal model in the univariateand multivariate cases. It is shown that the performance of this new prior model iscompetitive using various measures.

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