Universal nonuniform random vector generator based on acceptance-rejection

The acceptance/rejection approach is widely used in universal nonuniform random number generators. Its key part is an accurate approximation of a given probability density from above by a hat function. This article uses a piecewise constant hat function, whose values are overestimates of the density on the elements of the partition of the domain. It uses a sawtooth overestimate of Lipschitz continuous densities, and then examines all local maximizers of such an overestimate. The method is applicable to multivariate multimodal distributions. It exhibits relatively short preprocessing time and fast generation of random variates from a very large class of distributions.