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A probability density on a finite-dimensional Euclidean space is orthounimodal with a given mode if within each orthant (quadrant) defined by the mode, the density is a monotone function of each of its arguments individually. Up to a linear transformation, most of the commonly used random vectors possess orthounimodal densities. To generate a random vector from a given orthounimodal density, several general-purpose algorithms are presented; and an experimental performance evaluation illustrates the potential efficiency increases that can be achieved by these algorithms versus naive rejection.
Luc Devroye (Wed,) studied this question.