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Extended matrix variate gamma and beta functions

Author

Listed:
  • Nagar, Daya K.
  • Roldán-Correa, Alejandro
  • Gupta, Arjun K.

Abstract

The gamma and beta functions have been generalized in several ways. The multivariate beta and multivariate gamma functions due to Ingham and Siegel have been defined as integrals having the integrand as a scalar function of the real symmetric matrix. In this article, we define extended matrix variate gamma and extended matrix variate beta functions thereby generalizing multivariate gamma and multivariate beta functions defined by Ingham and Siegel. We study a number of properties of these newly defined functions. We also give some applications of these functions to statistical distribution theory.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:53-69
    DOI: 10.1016/j.jmva.2013.07.001
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    References listed on IDEAS

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    1. Hassairi, A. & Regaig, O., 2009. "Characterizations of the beta distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1682-1690, September.
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    Cited by:

    1. 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.
    2. Kołodziejek, Bartosz, 2016. "Characterization of beta distribution on symmetric cones," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 414-423.
    3. Daya K. Nagar & Alejandro Roldán-Correa & Saralees Nadarajah, 2023. "Expected Values of Scalar-Valued Functions of a Complex Wishart Matrix," Mathematics, MDPI, vol. 11(9), pages 1-14, May.
    4. Daya K. Nagar & Saralees Nadarajah & Idika E. Okorie, 2017. "A New Bivariate Distribution with One Marginal Defined on the Unit Interval," Annals of Data Science, Springer, vol. 4(3), pages 405-420, September.

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