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Matrix Variate Distribution Theory under Elliptical Models—V: The Non-Central Wishart and Inverted Wishart Distributions

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Abstract

The non-central Wishart and inverted Wishart distributions are studied in this work under elliptical models; some distributional results are based on some generalizations of the well-known Kummer relations, which leds us to determine that some moments have a polynomial representation. Then the non-central \(F\) and ‘‘studentized Wishart’’ distributions are derived in a general setting. After some generalizations, including the so called non-central generalized inverted Wishart distribution, the classical results based on Gaussian models are derived here as corollaries.

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ACKNOWLEDGMENT

This research work was supported by a joint project between the University of Medellin (Medellin, Colombia) and the Center for Mathematical Research (Guanajuato, Mexico). We are greatly thankful with the Editor and the Referees of this paper. Their carefully revisions and comments provided important improvement of the final version of this article.

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Authors and Affiliations

  1. Universidad de Medellín Faculty of Basic Sciences, Carrera 87 No.30-65, of. 4-216, Medellín, Colombia

    Francisco J. Caro-Lopera

  2. CIMAT A. C., Department of Probability and Statistics Callejón de Jalisco s/n, Mineral de Valenciana, 36240, Guanajuato, México

    Graciela González Farías

  3. McMaster University, Department of Mathematics and Statistics, L8S 4K1, Hamilton, Ontario, Canada

    N. Balakrishnan

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  1. Francisco J. Caro-Lopera
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  2. Graciela González Farías
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  3. N. Balakrishnan
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Correspondence to Francisco J. Caro-Lopera, Graciela González Farías or N. Balakrishnan.

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Caro-Lopera, F.J., González Farías, G. & Balakrishnan, N. Matrix Variate Distribution Theory under Elliptical Models—V: The Non-Central Wishart and Inverted Wishart Distributions. Math. Meth. Stat. 31, 18–42 (2022). https://doi.org/10.3103/S1066530722010021

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