论文信息 - On Multivariate Vertical Density Representation and its Application to Random Number Generation

On Multivariate Vertical Density Representation and its Application to Random Number Generation

Motivated by the works of Troutt (1991, 1993) and Kotz and Troutt (1996), we provide a multivariate definition of the vertical density representation (vdr) and calculate its value for some basic multivariate distributions presented in Fang et al. (1990) and Johnson (1987). Utilizing the multivariate vdr and the theorem of Troutt (1993) we generalize the well-known Box-Muller method to generate the basic multivariate distributions.

[1] Mark E. Johnson. Multivariate Statistical Simulation: Johnson/Multivariate , 1987 .

[2] Marvin D. Troutt,et al. A theorem on the density of the density ordinate and an alternative interpretation of the bqx-muller method , 1991 .

[3] Marvin D. Troutt. Vertical density representation and a further remark on the box-muller method , 1993 .

[4] Samuel Kotz,et al. On Vertical Density Representation and Ordering of Distributions , 1996 .

[5] M. E. Muller,et al. A Note on the Generation of Random Normal Deviates , 1958 .

[6] Chunsheng Ma,et al. Multivariate p-norm symmetric distributions , 1995 .

[7] S. Kotz,et al. Symmetric Multivariate and Related Distributions , 1989 .