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

TL;DR

This paper introduces the pattern block method, a generalized approach to the Ziggurat method, allowing efficient generation of random numbers from complex, multimodal, and multidimensional distributions.

Contribution

It reformulates and extends the Ziggurat method to handle a broader class of distributions, including multimodal and multidimensional cases.

Findings

Effective for multimodal distributions

Applicable to multidimensional random number generation

Demonstrated through multiple examples

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.