On the use of probability inequalities in random variate generation

Abstract

We show by example how various well-known probability inequalities can aid in the design of general nonuniform random variate generators, i.e. generators that can be used for large classes of densities. We obtain universal algorithms for the following classes:(1)all unimodal densities with mode at 0 and absolute rth moment not exceeding a known constant;(2)all densities satisfying a Lipschitz condition with known constant, having an absolute rth moment or a moment generating function in a neighborhood of 0 not exceeding a known constant. The algorithms assume that the density f can be computed at every point, but the distribution function is not needed.

Keywords:

• Probability Inequalities
• Random Variate Generation
• Simulation
• Acceptance/rejection Method
• Unimodality
• Chebyshev's Inequality
• Algorithms