Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

We review and discuss numerical inversion of the characteristic function as a tool for obtaining cumulative distribution functions. With the availability of high-speed computing and symbolic computation software, the method is ideally suited for instructional purposes, particularly in the illustration of the inversion theorems covered in graduate probability courses. The method is also available as an alternative to asymptotic approximations, Monte Carlo, or bootstrap techniques when analytic expressions for the distribution function are not available. We illustrate the method with several examples, including one which is concerned with the detection of possible clusters of disease in an epidemiologic study.