A Rejection Technique for Sampling from T-Concave Distributions

Abstract

rejection algorithm that uses a new method for constructing simple hat functions for a unimodal, bounded density f is introduced called “transformed density rejection.” It is based on the idea of transforming f with a suitable transformation T such that T(f(x)) is concave. f is then called T-concave, and tangents of T(f(x)) m the mode and in a point on the left and right side are used to construct a hat function with a table-mountain shape. It is possible to give conditions for the optimal choice of these points of contact. With the method can be used to construct a universal algorithm that is applicable to a large class of unimodal distributions, including the normal, beta, gamma, and t-distribution. © 1995, ACM. All rights reserved.