On an Approximation for Calculating Multivariate t Orthant Probabilities

  • Hea Jung Kim (Department of Statistics, Dongguk University, Seoul, 100-715, Korea)
  • Published : 1997.12.01

Abstract

An approximation for multivariate t probability for an orhant region(i.e., a rectangular resion with lower limits of $-\infty$ for all margins) is proposed. It is based on conditional expectations, a regression with binary variables, and the exact formula for the evalution of the bivariate t integrals by Dunnett and Sobel. It is noted that the proposed approximation method is espicially useful for evaluating the multivariate t integrals where there is no simple method available until now.

Keywords

References

  1. British Journal of Mathematical and Statistical Psychology v.45 Thurstonian representation for partial ranking data Bokenholt, U.
  2. Bayesian Inference in Statistical Analysis Box, G. E. P.;Tiao, G. C.
  3. Modelling Binary Data Collett, D.
  4. Technical Report No. 13, Division of Mathematical Statistics, Commonwealth Scientific and Industrial Research Organization The Multivariate t-distribution Associated with the General Multivariate Normal Distribution Cornish, E. A.
  5. Biometrika v.41 A bivariate generalization of Student's t-distribution, with tables for certain special cases Dunnett, C. W.;Sobel, M.
  6. Journal of Computational and Graphical Statistics v.1 Numerical computation of multivariate normal probabilities Genz, A.
  7. Biometrika v.48 On the evaluation of the probability integral of multivariate t-distribution John, S.
  8. Continuous Multivariate Distributions in Statistics Johnson, M. L.;Kotz, S.
  9. Journal of Statistical Computation and Simulation v.37 A method for approximating multivariate normal orthant probabilities Solow, A. R.
  10. Journal of the American Statistical Association v.90 Approximations to multivariate normal rectangle probabilities based on conditional expectation Joe, H.
  11. Bayesian Statistics Press, S. J.
  12. Journal of Statistical Computation and Simulation v.37 A method for approximating multivariate normal orthant probabilities Solow,A.R.