A Rejection Technique for Sampling from T-Concave Distributions

2024/01/18 by Hörmann, Wolfgang

paper · doi:10.57938/84b20557-bd15-4d6a-ab27-e4234ba465ef

Abstract

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/√(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. (author's abstract)

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