Unitary invariant and residual independent matrix distributions

Computational and Applied Mathematics

Volumn 28, Issue 1, 2009, Pages 63-86

  Gupta, Arjun K ^a   Nagar, Daya K ^b   Vélez Carvajal, Astrid M ^b  

^a BOWLING GREEN STATE UNIVERSITY   (United States)

^b UNIVERSIDAD DE ANTIOQUIA   (Colombia)

Author keywords

Beta distribution; Complex random matrix; Gauss hypergeometric function; Inverted complex Wishart; Residual independent; Unitary invariant; Zonal polynomial

Indexed keywords

BETA DISTRIBUTIONS; COMPLEX RANDOM MATRIX; GAUSS HYPERGEOMETRIC FUNCTION; INVERTED COMPLEX WISHART; MATRIX DISTRIBUTIONS; RESIDUAL INDEPENDENT; TYPE II; UNITARY INVARIANT; WISHART; ZONAL POLYNOMIALS;

EID: 69049094143     PISSN: 22383603     EISSN: 18070302     Source Type: Journal    
DOI: 10.1590/S0101-82052009000100004     Document Type: Article

References (18)

1. E. Bedoya, D.K. Nagar and A.K. Gupta, Moments of the complex matrix variate beta distribution. PanAmerican Mathematical Journal, 17(2) (2007), 21-32.
2. Y. Chikuse, Partial differential equations for hypergeometric functions of complex matrices and their applications. Annals of the Institute of Statistical Mathematics, 28 (1976), 187-199.
3. Xinping Cui, A.K. Gupta and D.K. Nagar, Wilks' factorization of the complex matrix variate Dirichlet distributions. Revista Matemática Complutense, 18(2) (2005), 315-328.
4. N.R. Goodman, Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Annals of Mathematical Statistics, 34 (1963), 152-177.
5. A.K. Gupta and D.K. Nagar, Matrix Variate Distributions. Chapman & Hall/CRC, Boca Raton (2000).
6. A.K. Gupta and D.K. Nagar, Product of independent complex Wishart matrices. International Journal of Statistics and System, 2(1) (2007), 59-73.
7. A.K. Gupta, D.K. Nagar and A.M. Vélez-Carvajal, Quadratic forms of independent complex beta matrices. International Journal of Applied Mathematics and Statistics, 13 (D08) (2008), 76-91.
8. A.T. James, Distributions of matrix variate and latent roots derived from normal samples. Annals of Mathematical Statistics, 35 (1964), 475-501.
9. C.G. Khatri, Classical statistical analysis based on a certain multivariate complex Gaussian distribution. Annals of Mathematical Statistics, 36 (1965), 98-114.
10. C.G. Khatri, On certain distribution problems based on positive definite quadratic functions in normal vectors. Annals of Mathematical Statistics, 37(2) (1966), 468-479.
11. C.G. Khatri, On the moments of traces of two matrices in three situations for complex multivariate normal populations. Sankhyā, A32 (1970), 65-80.
12. C.G. Khatri, R. Khattree and R.D. Gupta, On a class of orthogonal invariant and residual independent matrix distributions. Sankhy_a, B53(1) (1991), 1-10.
13. Y.L. Luke, The Special Functions and Their Approximations. Volume I, Academic Press, New York (1969).
14. D.K. Nagar, E. Bedoya and E.L. Arias, Non-central complex matrix-variate beta distribution. Advances and Applications in Statistics, 4(3) (2004), 287-302.
15. D.K. Nagar and A.K. Gupta, Expectations of functions of complex Wishart matrix. Applied Mathematics and Computations (submitted for publication).
16. P. Shaman, The inverted complex Wishart distribution and its application to spectral estimates. Journal of Multivariate Analysis, 10 (1980), 51-59.
17. W.Y. Tan, On the complex analogue of Bayesian estimation of a multivariate regression model. Annals of Institute of Statistical Mathematics, 25 (1973), 135-152.
18. W.Y. Tan, Some distribution theory associated with complex Gaussian distribution. Tamkang Journal, 7 (1968), 263-302.