The exact non-central distribution of the generalized variance

  • A. M. Mathai


Generalize Variance Exact Distribution Computable Form Generalize Hypergeometric Function Matrix Argument 


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  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

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© Institute of Statistical Mathematics 1972

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  • A. M. Mathai

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