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 algorithm 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.