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Matrix-variate Kummer-Beta distribution

Part of: Multivariate analysis Distribution theory

Published online by Cambridge University Press:  09 April 2009

Daya K. Nagar  and
Arjun K. Gupta
Daya K. Nagar
Affiliation:
Department de Matemáticas, Universidad de Antioquia, Medellín, A. A. 1226Colombia e-mail: [email protected]
Arjun K. Gupta
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403-0221, USA e-mail: [email protected]
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Abstract

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This paper proposes matrix variate generalization of Kummer-Beta family of distributions which has been studied recently by Ng and Kotz. This distribution is an extension of Beta distribution. Its characteristic function has been derived and it is shown that the distribution is orthogonally invariant. Some results on distribution of random quadratic forms have also been derived.

Keywords

confluent hypergeometric functioninvariant polynomialKummer-Beta distributionmatrix variatetransformationzonal polynomial

MSC classification

Secondary: 62H10: Distribution of statistics 62E15: Exact distribution theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 11 - 26
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Armero, C. and Bayarri, M. J., ‘A Bayesian analysis of a queuing system with unlimited service’, Technical Report No. 93–50, (Department of Statistics, Purdue University, 1993).Google Scholar
[2]Armero, C. and Bayarri, M. J., ‘A Bayesian analysis of a queuing system with unlimited service’, J. Statist. Plann. Inference 58 (1997), 241–264.Google Scholar
[3]Chikuse, Y., ‘Distributions of some matrix variates and latent roots in multivariate Behrens-Fisher discriminant analysis’, Ann. Statist. (2) 9 (1981), 401–407.Google Scholar
[4]Constantine, A. G., ‘Some non-central distribution problems in multivariate analysis’, Ann. Math. Statist. 34 (1963), 1270–1285.Google Scholar
[5]Davis, A. W., ‘Invariant polynomials with two matrix arguments extending the zonal polynomials: applications to multivariate distribution theory’, Ann. Inst. Statist. Math. 31 (1979), 465–485.Google Scholar
[6]Davis, A. W., ‘Invariant polynomials with two matrix arguments extending the zonal polynomials’, in: Multivariate analysis V (ed. Krishnaiah, P. R.) (North-Holland, Amsterdam, 1980) pp. 287–299.Google Scholar
[7]Gordy, M. B., ‘Computationally convenient distributional assumptions for common-value actions’, Comput. Econ. 12 (1998), 61–78.Google Scholar
[8]Gupta, A. K. and Nagar, D. K., ‘Matrix variate beta distribution’, Int. J. Math. Math. Sci. (7) 24 (2000), 449–459.Google Scholar
[9]Gupta, A. K. and Nagar, D. K., Matrix variate distributions (Chapman and Hall/CRC, Boca Raton, 2000).Google Scholar
[10]Javier, W. R. and Gupta, A. K., ‘On generalized matrix variate beta distributions’, Statistics (4) 16 (1985), 549–558.Google Scholar
[11]Ng, K. W. and Kotz, S., ‘Kummer-Gamma and Kummer-Beta univariate and multivariate distributions’, Research Report No. 84, (Department of Statistics, The University of Hong Kong, Hong Kong, 1995).Google Scholar
[12]Rao, C. R., Advanced statistical methods in biometric research (John Wiley and Sons, New York, 1952).Google Scholar