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A New Generalisation of Sam-Solai's Multivariate Additive Beta Distribution of Kind-2 of Type-A

Author Affiliations

  • 1Assistant Professor, Jamal Institute of Management, Tiruchirappalli, South India, INDIA
  • 2 Associate Professor, Dept. Of Mathematics, Jamal Mohamed college, Tiruchirappalli, South India, INDIA
  • 3 Assistant Professor, Jamal Institute of Management, Tiruchirappalli 620 020 South India, INDIA

Res. J. Management Sci., Volume 1, Issue (2), Pages 15-23, September,6 (2012)

Abstract

This paper proposed a new generalization of bounded continuous multivariate symmetric probability distributions. More specifically the authors visualizes a new generalization of Sam-Solais multivariate additive Beta distribution of Kind-2 of Type-A from the uni-variate two parameter Beta distribution of Kind-1. Further,we find its marginal, multivariate conditional distributions, multivariate generating functions, multivariate survival, hazard functions and also discussed its special cases. The special cases includes the transformation of Sam-Solais multivariate additive Beta distribution of Kind -2 of Type-A into multivariate additive Beta distribution of Kind-1 of Type-A, Multivariate F-distribution of Kind-1, Multivariate standard Logistic-Beta distribution of Kind-1. Moreover, it is found that the bivariate correlation between two Beta random variables purely depends on the shape parameter and we simulated and established selected standard bivariate Beta correlation bounds from 10,000 different combinations of values for shape parameter.

References

  1. Srivastava M.S.,on the distribution of a multiple correlation matrix, non-central Multivariate beta distributions, Ann. Math. Statist., 39, 277-232 (1968)
  2. W. Y. Tan, Note on the multivariate and the generalized multivariate beta distributions, J.Amer. Statist. Assoc. 64, 230241(1969)
  3. Khatri C.G. A note on Mitras paper A density-free approach to the matrix variate beta distribution, Sankhya Ser., A 32, 311318 (1970)
  4. Javier W.R. and Gupta A.K., On generalized matric variate beta distributions, Statistics, 16(4), 549558 (1985)
  5. Konno Y.,Exact moments of the multivariate F and beta distributions, J. Japan Statist. Soc., 18(2), 123130 (1988)
  6. Khattree R. and Gupta R.D.,some probability distributions connected with beta and Gamma matrices, Comm. Statist., Theory Methods,21(2), 369390 (1992)
  7. Uhlig H.,On singular Wishart and singular multivartiate beta distributions, Ann.Statistic., 22(15), 395-405 (1994)
  8. McDonald J.B. and Yexiao J. Xu, A generalization of the beta distribution with applications, Journal of Econometrics, 66, 133152 (1995)
  9. Gupta K. and Nagar D.K.,Matrix variate beta distribution,Int. J.Maths and Math. Sci., 23(7), 449459 (2000)
  10. Jones, M.C.Multivariate t and beta distributions associated with the multivariate F-distribution, Metrika, 54, 215-231 (2001)
  11. Nagar D.K. and Gupta A.K., Matrix variate Kummer-Beta distribution, Journal of Australian Mathematical Society, 73(1), 1125 (2002)
  12. Gupta K. and Nadarajah S. (Eds.), Handbook of Beta Distribution and Its Applications, New York, Marcel Dekker (2004)
  13. Nadarajah S. and Kotz S., Some beta distributions, Bulletin of the Brazilian Mathematical Society, New Series, 37(1), 103125 (2006)
  14. D'iaz-Garcia J.A. and Gutierrez-Jaimez R.,Non-central, nonsingular matrix variate beta distribution, Brazilian J. Prob. Statist.21, 175186 (2007)