2001-03.wh
#
A Note on the Performance of the "Ahrens Algorithm"

### Abstract

This short note discusses performance bounds for "Ahrens" algorithm,
that can generate random variates from continuous distributions
with monotonically decreasing density. This rejection algorithms
uses constant hat-functions and constant squeezes over many
small intervals. The choice of these intervals is important.
Ahrens has demonstrated that the equal area rule that uses strips of
constant area leads to a very simple algorithm. We present bounds
on the rejection constant of this algorithm depending only on the number
of intervals.

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

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

**General Terms:**
Algorithms

**Key Words:**
random variate generation, rejection method,
universal generator, performance measures

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Paper

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