Pattern block method for generating random numbers : Reformulation and generalization of the Ziggurat method using conditional random variables

Abstract

The Ziggurat method is an efficient rejection sampling technique for generating one-dimensional normally distributed random numbers. This study proposes the pattern block method, a generalization of the Ziggurat method. The pattern block method enables the generation of random numbers from multimodal density functions and multidimensional distributions. The effectiveness of the pattern block method is demonstrated through several examples.