Skip to main content
SpringerLink
Log in

Matricvariate and matrix multivariate T distributions and associated distributions

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

Several distributions are studied, simultaneously in the real, complex, quaternion and octonion cases. Specifically, these are the central, nonsingular matricvariate and matrix multivariate T and beta type II distributions and the joint density of the singular values are obtained for real normed division algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Baez JC (2002) The octonions. Bull Am Math Soc 39: 145–205

    Article  MathSciNet  MATH  Google Scholar 

  • Díaz-García JA, Gutiérrez-Jáimez R (2006) The distribution of the residual from a general elliptical multivariate linear regression model. J Multivar Anal 97: 1829–1841

    Article  MATH  Google Scholar 

  • Díaz-García JA, Gutiérrez-Jáimez R (2009a) Random matrix theory and multivariate statistics. http://arxiv.org/abs/0907.1064. Also submited

  • Díaz-García JA, Gutiérrez-Jáimez R (2009) Singular matric and matrix variate t distributions. J Stat Plan Inference 139: 2382–2387

    Article  MATH  Google Scholar 

  • Díaz-García JA, Gutiérrez-Jáimez R (2011) On Wishart distribution. Linear Algebra Appl. doi:10.1016/j.laa.2011.03.007

  • Díaz-García JA, Ramos-Quiroga R (2003) Generalised natural conjugate prior densities: singular multivariate linear model. Int Math J 3(12): 1279–1287

    MathSciNet  MATH  Google Scholar 

  • Dickey JM (1967) Matricvariate generalizations of the multivariate t-distribution and the inverted multivariate t-distribution. Ann Math Stat 38: 511–518

    Article  MathSciNet  MATH  Google Scholar 

  • Edelman A, Rao RR (2005) Random matrix theory. Acta Numerica 14: 233–297

    Article  MathSciNet  MATH  Google Scholar 

  • Fang KT, Zhang YT (1990) Generalized multivariate analysis. Science Press, Springer, Beijing

    MATH  Google Scholar 

  • Forrester PJ (2009) Log-gases and random matrices. To appear. Available in: http://www.ms.unimelb.edu.au/~matpjf/matpjf.html

  • Goodall CR, Mardia KV (1993) Multivariate aspects of shape theory. Ann Stat 21: 848–866

    Article  MathSciNet  MATH  Google Scholar 

  • Gross KI, Richards DP St P (1987) Special functions of matrix argument I: algebraic induction zonal polynomials and hypergeometric functions. Trans Am Math Soc 301(2): 475–501

    MathSciNet  Google Scholar 

  • Gupta AK, Nagar DK (2000) Matrix variate distributions. Chapman & Hall/CR, New York

    MATH  Google Scholar 

  • Herz CS (1995) Bessel functions of matrix argument. Ann Math 61(3): 474–523

    Article  MathSciNet  Google Scholar 

  • James AT (1964) Distribution of matrix variate and latent roots derived from normal samples. Ann Math Stat 35: 475–501

    Article  MATH  Google Scholar 

  • Kabe DG (1984) Classical statistical analysis based on a certain hypercomplex multivariate normal distribution. Metrika 31: 63–76

    Article  MathSciNet  MATH  Google Scholar 

  • Khatri CG (1970) A note on Mitra’s paper “A density free approach to the matrix variate beta distribution”. Sankhyā A 32: 311–318

    MATH  Google Scholar 

  • Kotz S, Nadarajah S (2004) Multivariate t distributions and their applications. Cambridge University Press, UK

    Book  MATH  Google Scholar 

  • Li F, Xue Y (2009) Zonal polynomials and hypergeometric functions of quaternion matrix argument. Commun Stat Theory Methods 38(8): 1184–1206

    Article  MathSciNet  MATH  Google Scholar 

  • Mehta ML (1991) Random matrices, 2nd edn. Academic Press, Boston

    MATH  Google Scholar 

  • Micheas AC, Dey DK, Mardia KV (2006) Complex elliptical distribution with application to shape theory. J Stat Plan Inference 136: 2961–2982

    Article  MathSciNet  MATH  Google Scholar 

  • Muirhead RJ (1982) Aspects of multivariate statistical theory. Wiley, New York

    Book  MATH  Google Scholar 

  • Press SJ (1982) Applied multivariate analysis: using bayesian and frequentist methods of inference, 2nd edn. Robert E. Krieger Publishing Company, Malabar

    MATH  Google Scholar 

  • Ratnarajah T, Vaillancourt R, Alvo A (2005) Complex random matrices and Rician channel capacity. Probl Inf Transm 41(1): 1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Srivastava SM, Khatri CG (1979) An introduction to multivariate statistics. North Holland, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Computation, Universidad Autónoma Agraria Antonio Narro, 25315, Buenavista, Saltillo, Coahuila, Mexico

    José A. Díaz-García

  2. Department of Statistics and O. R., University of Granada, 18071, Granada, Spain

    Ramón Gutiérrez-Jáimez

Authors
  1. José A. Díaz-García
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramón Gutiérrez-Jáimez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José A. Díaz-García.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Díaz-García, J.A., Gutiérrez-Jáimez, R. Matricvariate and matrix multivariate T distributions and associated distributions. Metrika 75, 963–976 (2012). https://doi.org/10.1007/s00184-011-0362-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-011-0362-8

Keywords

Search

Navigation