A Rejection Technique for Sampling from T-Concave Distributions

A rejection algorithm { called transformed density rejection { that uses a new method for constructing simple hat functions for an unimodal, bounded density f is introduced. It is based on the idea to transform 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)) in the mode and in a point on the left and right side are used to construct a hat function with table-mountain shape. It is possible to give conditions for the optimal choice of these points of contact. With T = ?1= p x 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.