Automatic sampling with the ratio-of-uniforms method

Applying the ratio-of-uniforms method for generating random variates result s in very efficient, fast, and easy-to-implement algorithms. However parame ters for every particular type of density must be precalculated analyticall y. In this article we show, that the ratio-of-uniforms method is also usefu l for the design of a black-box algorithm suitable for a large class of dis tributions, including all with log-concave densities. Using polygonal envel opes and squeezes results in an algorithm that is extremely fast. In opposi tion to any other ratio-of-uniforms algorithm the expected number of unifor m random numbers is less than two. Furthermore, we show that this method is in some sense equivalent to transformed density rejection.