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Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions

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  • Daya K. Nagar
  • Raúl Alejandro Morán-Vásquez
  • Arjun K. Gupta

Abstract

Hypergeometric functions of matrix arguments occur frequently in multivariate statistical analysis. In this paper, we define and study extended forms of Gauss and confluent hypergeometric functions of matrix arguments and show that they occur naturally in statistical distribution theory.

Suggested Citation

  • Daya K. Nagar & Raúl Alejandro Morán-Vásquez & Arjun K. Gupta, 2015. "Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:190723
    DOI: 10.1155/2015/190723
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    References listed on IDEAS

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    1. Bekker, A. & Roux, J.J.J. & Ehlers, R. & Arashi, M., 2012. "Distribution of the product of determinants of noncentral bimatrix beta variates," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 73-87.
    2. Nagar, Daya K. & Roldán-Correa, Alejandro & Gupta, Arjun K., 2013. "Extended matrix variate gamma and beta functions," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 53-69.
    3. Butler, Ronald W. & Wood, Andrew T.A., 2005. "Laplace approximations to hypergeometric functions of two matrix arguments," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 1-18, May.
    4. Hashiguchi, Hiroki & Numata, Yasuhide & Takayama, Nobuki & Takemura, Akimichi, 2013. "The holonomic gradient method for the distribution function of the largest root of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 296-312.
    5. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
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