OBTAINING DISTRIBUTION-FUNCTIONS BY NUMERICAL INVERSION OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS

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