Random variate generation for multivariate unimodal densities

ABSTRACT

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.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Random number generation

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Algorithms, Experimentation, Measurement, Verification

Keywords:
multivariate densities, nonparametric classes, random variate generation, unimodality