this paper we introduce an new approach for universal bounding curves based on the ratio-of-uniforms method. The new algorithm is even simpler and can be applied to a larger class of distributions, including all log-concave distributions. As for Devroye's algorithm the expected number of uniform random numbers does not depend on the particular distribution. In opposition to other black-box algorithms hardly any setup step is required. Thus it is superior in the changing parameter chase.

This paper presents an overview of the most powerful universal methods. These are based on acceptance/rejection techniques where hat and squeezes are constructed automatically. Although originally motivated to sample from non-standard distributions these methods have advantages that make them attractive even for sampling from standard distributions and thus are an alternative to special generators tailored for particular distributions. Most important are: the marginal generation time is fast and does not depend on the distribution. They can be used for variance reduction techniques, and they produce random numbers of predictable quality. These algorithms are implemented in a library, called UNURAN, which is available by anonymous ftp.

Abstract. We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions for a particular generator. The algorithms can be implemented in a few lines of high level language code. 1.