Research ArticleNo Access

On characterizing the complex Wishart distribution

Imen Boutouria

Laboratory of Probability and Statistics, Sfax University, B.P. 1171, Tunisia

E-mail Address: imen.boutouria@fss.rnu.tn

https://doi.org/10.1142/S1793557122500851Cited by:0 (Source: Crossref)

Abstract

In this research paper, we generalized the results of Ignacy in the multivariate case in order to characterize the complex Wishart distribution.

Communicated by H. M. Srivastava

Keywords:

AMSC: 60A10, 60B20

References

1. I. Boutouria , Characterization of the Wishart distributions on homogeneous cones, Comptes Rendus Math. 341(1) (2005) 43–48. Crossref, Web of Science, Google Scholar
2. I. Boutouria , Characterization of the Wishart distribution on Homogeneous cones in the Bobecka and Wesołowski way, Commun. Stat. Theory Methods 38(15) (2009) 2552–2566. Crossref, Web of Science, Google Scholar
3. B. V. Bronk , Ensemble for random matrices, J. Math. Phys. 6(2) (1965) 228–237. Crossref, Web of Science, Google Scholar
4. D. R. Brillinger , Asymptotic properties of spectral estimates of second order, Biometrika 56 (1969) 375–390. Crossref, Web of Science, Google Scholar
5. M. Carmeli , Statistical Theory and Random Matrices, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 74 (Marcel Dekker, New York, 1983). Google Scholar
6. Y. Chikuse , Partial differential equations for hypergeometric functions of complex argument matrices and their applications, Ann. Inst. Stat. Math. 28(2) (1976) 187–199. Crossref, Google Scholar
7. N. R. Goodman , Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction), Ann. Math. Stat. 34 (1963) 152–177. Crossref, Google Scholar
8. T. Hayakawa , On the distribution of the latent roots of a complex Wishart matrix (non-central case), Ann. Inst. Statist. Math. 24 (1972) 1–17. Crossref, Web of Science, Google Scholar
9. I. I. Kotlarski , On characterizing the Gamma and the normal distribution, Pacific J. Math. 20(1) (1967) 69–76. Crossref, Web of Science, Google Scholar
10. A. T. James , Distributions of matrix variates and latent roots derived from normal samples, Ann. Math. Stat. 35 (1964) 475–501. Crossref, Google Scholar
11. C. G. Khatri , Classical statistical analysis based on a certain multivariate complex Gaussian distribution, Ann. Math. Stat. 36 (1965) 98–114. Crossref, Google Scholar
12. P. R. Krishnaiah , Some recent developments on complex multivariate distributions, J. Multivariate Anal. 6(1) (1976) 1–30. Crossref, Web of Science, Google Scholar
13. I. Olkin and H. Rubin, Multivariate beta distributions and independence properties of the Wishart distribution, Ann. Math. Stat. 35 (1964) 261–269. Erratum 37(1) (1966) 297. Google Scholar
14. M. S. Srivastava , On the complex Wishart distribution, Ann. Math. Statist. 36 (1965) 313–315. Crossref, Google Scholar
15. E. Lukas , A characterization of the gamma distribution, Ann. Math. Statist. 26 (1955) 319–324. Crossref, Google Scholar
16. W. Y. Tan , Some distribution theory associated with complex Gaussian distribution, Tamkang J. 7 (1968) 263–302. Google Scholar
17. W. Y. Tan , Note on the multivariate and the generalized multivariate beta distributions, J. Am. Stat. Assoc. 64 (1969) 230–241. Crossref, Web of Science, Google Scholar
18. R. A. Wooding , The multivariate distribution of complex normal variables, Biometrika 43 (1956) 212–215. Crossref, Web of Science, Google Scholar
19. X. Cui, K. Arjun Gupta and Daya K. Nagar , Wilks’ factorization of the complex matrix Variate Dirichlet distributions, Rev. Mat. Complut. 18(2) (2005) 315–328. Crossref, Google Scholar