# A Rejection Technique for Sampling from T-Concave Distributions

Wolfgang Hörmann

Publication: Working/Discussion PaperWU Working Paper

## 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 $T=-1/\sqrt(x)$ 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)
Original language English Vienna Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business Published - 1994

### Publication series

Name Preprint Series / Department of Applied Statistics and Data Processing 11

## WU Working Paper Series

• Preprint Series / Department of Applied Statistics and Data Processing