Some complex matrix-variate statistical distributions on rectangular matrices

Linear Algebra and Its Applications

Volumn 410, Issue 1-3, 2005, Pages 198-216

  Mathai, A M ^a   Provost, Serge B ^b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Beta distribution; Complex variate distributions; Dirichlet distribution; Gamma distribution; Random matrices; Rectangular matrices

Indexed keywords

MULTIVARIABLE CONTROL SYSTEMS; PROBABILITY; RANDOM PROCESSES;

BETA DISTRIBUTION; COMPLEX-VARIATE DISTRIBUTIONS; DIRICHLET DISTRIBUTION; GAMMA DISTRIBUTION; RANDOM MATRICES; RECTANGULAR MATRICES;

MATRIX ALGEBRA;

EID: 27344445629     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.07.016     Document Type: Conference Paper

References (26)

1. T. Berger On the correlation coefficient of a bivariate, equal variance, complex Gaussian sample Ann. Math. Statist. 43 1972 2000 2003
2. D.R. Brillinger Asymptotic properties of spectral estimates of second order Biometrika 56 1969 375 390
3. M. Carmeli Statistical Theory and Random Matrices in Physics 1983 Marcel Dekker New York
4. N.R. Goodman Statistical analysis based on a certain multivariate complex Gaussian distribution (An introduction) Ann. Math. Statist. 34 1963 152 177
5. N.R. Goodman The distribution of the determinant of a complex Wishart distributed matrix Ann. Math. Statist. 34 1963 178 180
6. R.D. Gupta, and D.St.P. Richards Multivariate Liouville distributions J. Multivariate Anal. 23 1987 233 256
7. T. Hayakawa The asymptotic distributions of the statistics based on the complex Gaussian distribution Ann. Inst. Statist. Math. 24 1972 231 244
8. C.G. Khatri Classical statistical analysis based on a certain multivariate complex Gaussian distribution Ann. Math. Statist. 36 1965 98 114
9. C. Kooperberg, and F. O'Sullivan Predictive oscillation patterns: a synthesis of methods for spatial-temporal decomposition of random fields J. Am. Statist. Assoc. 91 1996 1485 1496
10. P.R. Krishnaiah, J.C. Lee, and T.C. Chang The distributions of the likelihood ratio statistics for tests of certain covariance structures of complex multivariate normal populations Biometrika 63 1976 543 549
11. H.C. Li, K.C.S. Pillai, and T.C. Chang Asymptotic expansions for distributions of the roots of two matrices from classical and complex Gaussian populations Ann. Math. Statist. 41 1970 1541 1556
12. I.B. MacNeill Tests for periodic components in multiple time series Biometrika 61 1974 57 70
13. A.M. Mathai Jacobians of Matrix Transformations and Functions of Matrix Argument 1997 World Scientific New Jersey
14. A.M. Mathai An Introduction to Geometrical Probability: Distributional Aspects with Applications 1999 Gordon and Breach Scientific Publishers New York
15. A.M. Mathai A pathway to matrix-variate gamma and normal densities Linear Algebra Appl. 396 2005 317 328
16. M.L. Mehta Random Matrices second ed. 1991 Academic Press New York
17. R. Mohanty, and M. Pourahmadi Estimation of the generalized prediction error variance of a multiple time series J. Am. Statist. Assoc. 91 1996 294 299
18. R. Nagar, and E.L. Arias Complex matrix-variate Cauchy distribution Sci. Math. Jpn. 58 1 2003 67 80
19. I. Olkin, On distribution problems in multivariate analysis, Doctoral dissertation, University of North Carolina, Institute of Statistics, Mimeograph Series No. 43, pp. 1-126, 1951.
20. I. Olkin Note on 'The Jacobians of certain matrix transformations useful in multivariate analysis' Biometrika 40 1953 43 46
21. I. Olkin The 70th anniversary of the distribution of random matrices: A survey Linear Algebra Appl. 354 2002 231 243
22. I. Olkin, and A.R. Sampson Jacobians of matrix transformations and induced functional equations Linear Algebra Appl. 5 1972 257 276
23. K.C.S. Pillai, and B.N. Nagarsenker On the distribution of the sphericity test criterion in classical and complex normal populations having unknown covariance matrices Ann. Math. Statist. 42 1971 764 767
24. G.L. Turin The characteristic function of Hermitian quadratic forms in complex normal variables Biometrika 47 1960 199 201
25. G. Wahba Some tests of independence for stationary multivariate time series J. Roy. Statist. Soc. B 33 1971 153 166
26. R.A. Wooding The multivariate distribution of complex normal variables Biometrika 43 1956 212 215