A rejection technique for sampling from T -concave distributions
- 1 June 1995
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 21 (2) , 182-193
- https://doi.org/10.1145/203082.203089
Abstract
A 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)) in 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 T = -1/xxx, 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.Keywords
This publication has 19 references indexed in Scilit:
- A universal generator for discrete log-concave distributionsComputing, 1994
- Adaptive Rejection Sampling for Gibbs SamplingJournal of the Royal Statistical Society Series C: Applied Statistics, 1992
- The ACR method for generating normal random variablesOR Spectrum, 1990
- A simple generator for discrete log-concave distributionsComputing, 1987
- Non-Uniform Random Variate GenerationPublished by Springer Nature ,1986
- The Simulation of Generalized Inverse Gaussian and Hyperbolic Random VariablesSIAM Journal on Scientific and Statistical Computing, 1982
- Generating gamma variates by a modified rejection techniqueCommunications of the ACM, 1982
- Computer methods for efficient sampling from largely arbitrary statistical distributionsComputing, 1981
- Generating beta variates with nonintegral shape parametersCommunications of the ACM, 1978
- The Generation of Gamma Variables with Non-Integral Shape ParameterJournal of the Royal Statistical Society Series C: Applied Statistics, 1977