94-03-01.wh
#
A Rejection Technique for sampling from T-Concave Distributions

### 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.

**Mathematics Subject Classification:**
65C10 (Random Number Generation),
68C25

**CR Categories and Subject Descriptors:**
G.3 [Probability and Statistics]: Random number generation

**General Terms:**
Algorithms

**Key Words:**
random number generation, rejection method, log-concave density,
universal method

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© ACM, (1995). This is the author's version of the work.
It is posted here by permission of ACM for your personal use.
Not for redistribution. The definitive version was published in
Trans. Math. Softw. 21(2), 182-193.
http://doi.acm.org/10.1145/203082.203089

Paper

Wolfgang.Hoermann@statistik.wu-wien.ac.at