The Integration of the Multivariate Normal Density Function for the Triangular Method
作者： John A. Kapenga , Kenneth Mullen , Elise Doncker , Daniel M. Ennis
DOI: 10.1007/978-94-009-3889-2_30
关键词: Multivariate normal distribution 、 Multivariate stable distribution 、 Probability density function 、 Normal distribution 、 Matrix t-distribution 、 Mathematical analysis 、 Mathematics 、 Matrix normal distribution
摘要: The model involved in the triangular method is presented, which leads to need for evaluating a multidimensional integral of normal density function over an irregular region. Work done on numerical evaluation this discussed.
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sci-hub.st 参考文章(14)
J. J. Dongarra, C. B. Moler, G. W. Stewart, J. R. Bunch, LINPACK Users' Guide ,(1987)
Daniel M. Ennis, Kenneth Mullen, A multivariate model for discrimination methods Journal of Mathematical Psychology. ,vol. 30, pp. 206- 219 ,(1986) , 10.1016/0022-2496(86)90014-3
David Kahaner, Webb Wyman, Mathematical Software in Basic Evaluation of Definite Integrals IEEE Micro. ,vol. 3, pp. 42- 46 ,(1983) , 10.1109/MM.1983.291166
Daniel M. Ennis, Keneth Mullen, The effect of dimensionality on results from the triangular method Chemical Senses. ,vol. 10, pp. 605- 608 ,(1985) , 10.1093/CHEMSE/10.4.605
J. E. R. Frijters, Variations of the triangular method and the relationship of its unidimensional probabilistic models to three‐alternative forced‐choice signal detection theory models British Journal of Mathematical and Statistical Psychology. ,vol. 32, pp. 229- 241 ,(1979) , 10.1111/J.2044-8317.1979.TB00595.X
A.C. Genz, A.A. Malik, Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region Journal of Computational and Applied Mathematics. ,vol. 6, pp. 295- 302 ,(1980) , 10.1016/0771-050X(80)90039-X
J. N. Lyness, When Not to Use an Automatic Quadrature Routine SIAM Review. ,vol. 25, pp. 63- 87 ,(1983) , 10.1137/1025003
T. W. Sag, G. Szekeres, Numerical evaluation of high-dimensional integrals Mathematics of Computation. ,vol. 18, pp. 245- 253 ,(1964) , 10.1090/S0025-5718-1964-0165689-X
W. G., A. H. Stroud, Approximate calculation of multiple integrals Mathematics of Computation. ,vol. 27, pp. 437- ,(1973) , 10.2307/2005635
Kenneth Mullen, Daniel M. Ennis, Mathematical formulation of multivariate euclidean models for discrimination methods Psychometrika. ,vol. 52, pp. 235- 249 ,(1987) , 10.1007/BF02294237