Generation of multivariate distributions by vertical density representation

Troutt (1991, 1993) proposed the idea of the vertical density representatio n (VDR) based on Box-Mular method. Kotz, Fang and Liang (1997) provided a s ystematic study on the multivariate vertical density representation (MVDR). Suppose that we want to generate a random vector X is an element of R-n th at has a density function f(x). The key point of using the MVDR is to gener ate the uniform distribution on (S) over barf (v) = {x :f(x) = v} for any v > 0 which is the surface in R-n. In this paper we use the conditional dist ribution method to generate the uniform distribution on a domain or on some surface and based on it we proposed an alternative version of the MVDR(typ e 2 MVDR), by which one can transfer the problem of generating a random vec tor X with given density f to one of generating (X, Xn+1) that follows the uniform distribution on a region in Rn+1 defined byf. Several examples indi cate that the proposed method is quite practical.