Methods for generating random variates with Polya characteristic functions (Q1060522)

This paper shows that there exists a simple general method of random variate generation for distributions with Polya-characteristic functions; i.e. real even continuous functions \(\phi\) with \(\phi (0)=1\), \(\lim_{t\to \infty}\phi (t)=0,\) convex on (0,\(\infty)\). The procedure requires the explicit knowledge of \(\phi\) and at least one derivative of \(\phi\), but no knowledge of explicit form of the density or distribution function. As examples, the symmetric stable distributions, Linnik's distribution and a few other distributions are discussed.