Volume 20, Issue 1 (6-2021)                   JIRSS 2021, 20(1): 289-306 | Back to browse issues page

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University of Pretoria, Department of Statistics, Pretoria, South Africa , Andriette.Bekker@up.ac.za
Abstract:   (616 Views)

Matrix-variate beta distributions are applied in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. A methodology is proposed to generate matrix-variate beta generator distributions by combining the matrix-variate beta kernel with an unknown function of the trace operator. Several statistical characteristics, extensions and developments are presented. Special members are then used in a univariate and multivariate Bayesian analysis setting. These models are fitted to simulated and real datasets, and their fitting and performance are compared to well-established competitors.

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Type of Study: Special Issue, Original Paper | Subject: 62Exx: Distribution theory
Received: 2020/11/24 | Accepted: 2021/02/7 | Published: 2021/06/20

1. Bekker, A., Roux, J. J. J., Ehlers, R., and Arashi, M. (2012), Distribution of the product of determinants of noncentral bimatrix beta variates. Journal of Multivariate Analysis, 109, 73-87. [DOI:10.1016/j.jmva.2012.02.016]
2. Bekker, A., Van Niekerk, J., and Arashi, M. (2017), Wishart distributions: Advances in theory with Bayesian application. Journal of Multivariate Analysis, 155, 272-283. [DOI:10.1016/j.jmva.2016.12.002]
3. Chikuse, Y. (1980), Invariant polynomials with matrix arguments and their applications. Multivariate Statistical Analysis, 1, 54-68.
4. Davis, A. W. (1979), Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory. Annals of the Institute of Statistical Mathematics, 31(A), 465-485. [DOI:10.1007/BF02480302]
5. Ehlers, R. (2011), Bimatrix Variate Distributions of Wishart Ratios With Application. Unpublished PhD Dissertation, University of Pretoria, South Africa.
6. Gupta, A.K. and Nagar, D.K. (2000), Matrix-variate beta distribution. International Journal of Mathematical Sciences, 24(7), 449-459. [DOI:10.1155/S0161171200002398]
7. Gupta, A. K., and Nagar, D. K. (2006), A generalized matrix-variate beta distribution. International Journal of Applied Mathematical Sciences, 31(1), 21-36.
8. Gupta, A. K., and Nagar, D. K. (2009), Properties of matrix-variate beta type 3 distribution. International Journal of Mathematical Sciences, http://dx.doi.org/10.1155/2009/308518. [DOI:10.1155/2009/308518]
9. Muirhead, R. J. (2005), Aspects of Multivariate Statistical Theory. New York: Wiley.
10. Nadarajah, S., and Kotz, S. (2006), Some beta distributions. Bulletin of the Brazilian Mathematical Society, 31(1), 103-125. [DOI:10.1007/s00574-006-0006-1]
11. Nagar, D. K., and Gupta, A. K. (2002), Matrix-variate Kummer-beta distribution. Journal of the Australian Mathematical Society, 73(1), 11-26. [DOI:10.1017/S1446788700008442]
12. Nagar, D. K., Rold'a-Correa, A., and Gupta, A. K. (2013), Extended matrix-variate gamma and beta functions. Journal of Multivariate Analysis, 122, 53-69. [DOI:10.1016/j.jmva.2013.07.001]
13. Nagar, D. K., Arashi, M., and Nadarajah, S. (2017), Bimatrix variate gamma-beta distributions. Communications in Statistics - Theory and Methods, 46(9), 4464-4483. [DOI:10.1080/03610926.2015.1085562]
14. Ng, K. W., and Kotz, S. (1995), Kummer-gamma and Kummer-beta univariate and multivariate distributions. Research report, The University of Hong Kong, Hong Kong.
15. Pham-Gia, T., Phong, D. T., and Thanh, D. N. (2020), Distributions of powers of the central beta matrix variates and applications. Statistical Methods and Applications, 29(3), 651-668. [DOI:10.1007/s10260-019-00497-3]
16. Tounsi, M. (2019), The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices. Methodology and Computing in Applied Probability,1-30.
17. Zine, R. (2012), On the matrix-variate beta distribution. Communications in Statistics- Theory and Methodology, 41(9), 1569-1582. [DOI:10.1080/03610926.2010.546545]

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