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Wishart distributions: Advances in theory with Bayesian application

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  • Bekker, Andriëtte
  • van Niekerk, Janet
  • Arashi, Mohammad

Abstract

In this paper, we generalize the Wishart distribution utilizing a fresh approach that leads to the hypergeometric Wishart generator distribution with the Wishart generator and the Wishart as special cases. Important statistical characteristics are derived. The significance of this generator distribution is further demonstrated by assuming a special case as a prior for the underlying matrix variate normal model.

Suggested Citation

  • Bekker, Andriëtte & van Niekerk, Janet & Arashi, Mohammad, 2017. "Wishart distributions: Advances in theory with Bayesian application," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 272-283.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:272-283
    DOI: 10.1016/j.jmva.2016.12.002
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    References listed on IDEAS

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    1. Alberto Roverato, 2002. "Hyper Inverse Wishart Distribution for Non‐decomposable Graphs and its Application to Bayesian Inference for Gaussian Graphical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 391-411, September.
    2. Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    3. Hao Wang & Mike West, 2009. "Bayesian analysis of matrix normal graphical models," Biometrika, Biometrika Trust, vol. 96(4), pages 821-834.
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