The exact non-central distribution of the generalized variance

  • A. M. Mathai
Article

Keywords

Generalize Variance Exact Distribution Computable Form Generalize Hypergeometric Function Matrix Argument 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Anderson, T. W. (1946). The non-central Wishart distribution and certain problems of multivariate statistics,Ann. Math. Statist.,17, 409–431.MATHGoogle Scholar
  2. [2]
    Anderson, T. W. (1958).Introduction to Multivariate Statistical Analysis, Wiley, New York.Google Scholar
  3. [3]
    Bagai, O. P. (1962). Distribution of the determinant of the sum of products matrix in the non-central case for some values ofp, Sankhya, Ser. A,24, 55–62.MATHMathSciNetGoogle Scholar
  4. [4]
    Bagai, O. P. (1964). Limiting distributions of some statistics in multivariate analysis of variance,Sankhya, Ser. A,26, 271–278.MathSciNetGoogle Scholar
  5. [5]
    Bagai, O. P. (1965). The distribution of the generalized variance,Ann. Math. Statist.,36, 120–130.MATHMathSciNetGoogle Scholar
  6. [6]
    Braaksma, B. L. J. (1963). Asymptotic expansions and analytic continuations for a class of Barnes-integrals,Compositio Mathematica,15, 239–341.MATHMathSciNetGoogle Scholar
  7. [7]
    Constantine, A. G. (1963). Some non-central distribution problem in multivariate analysis,Ann. Math. Statist.,34, 1270–1285.MATHMathSciNetGoogle Scholar
  8. [8]
    Consul, P. C. (1964). On the limiting distributions of some statistics proposed for tests of hypotheses,Sankhya, Ser. A,26, 279–286.MATHMathSciNetGoogle Scholar
  9. [9]
    Consul, P. C. (1964–65). Distribution of the determinant of the sum of product matrix in the non-central linear case,Mathematische Nachrichten,28, 169–179.MathSciNetGoogle Scholar
  10. [10]
    Erdélyi, A., et al. (1953).Higher Transcendental Functions, Vol. I, McGraw-Hill, New York.MATHGoogle Scholar
  11. [11]
    Fujikoshi, Y. (1967). Asymptotic expansion of the generalized variance, (Reported in the meeting of Math. Soc., Japan, October).Google Scholar
  12. [12]
    Herz, C. S. (1955). Bessel functions of matrix arguments,Ann. Math.,61, 474–523.MATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    James, A. T. (1954). Normal multivariate analysis and the orthogonal group,Ann. Math. Statist.,25, 40–75.MATHGoogle Scholar
  14. [14]
    James, A. T. (1961). Zenal polynomials of the real positive definite symmetric matrices,Ann. Math.,74, 456–469.MATHCrossRefGoogle Scholar
  15. [15]
    Mathai, A. M. and Rathie, P. N. (1971). The exact distribution of the generalized variance in the non-central linear case,Sankhya, Ser. A,33, to appear.Google Scholar
  16. [16]
    Rao, C. R. (1965).Linear Statistical Inference and Its Applications, Wiley, New York.MATHGoogle Scholar
  17. [17]
    Sugiura, N. and Fujikoshi, Y. (1969). Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence.Ann. Math. Statist.,40, 942–952.MATHMathSciNetGoogle Scholar
  18. [18]
    Wilks, S. S. (1932). Certain generalizations in the analysis of variance,Biometrika,24, 471–494.MATHCrossRefGoogle Scholar

Copyright information

© Institute of Statistical Mathematics 1972

Authors and Affiliations

  • A. M. Mathai

There are no affiliations available

Personalised recommendations