Generation of multivariate distributions by vertical density representation

Abstract

Troutt (1991,1993) proposed the idea of the vertical density representation (VDR) based on Box-Millar method. Kotz, Fang and Liang (1997) provided a systematic study on the multivariate vertical density representation (MVDR). Suppose that we want to generate a random vector X[d]Rnthat has a density function ƒ(x). The key point of using the MVDR is to generate the uniform distribution on [D]ƒ(v) = {x :ƒ(x) = v} for any v > 0 which is the surface in RnIn this paper we use the conditional distribution 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(type 2 MVDR), by which one can transfer the problem of generating a random vector X with given density f to one of generating (X, Xn+i) that follows the uniform distribution on a region in Rn+1defined by ƒ. Several examples indicate that the proposed method is quite practical.