Computer Generation of Statistical Distributions

This report presents a collection of computer-generated statistical distributions which are useful for performing Monte Carlo simulations. The distributions are encapsulated into a C++ class, called "Random", so that they can be used with any C++ program. The class currently contains 27 continuous distributions, 9 discrete distributions, data-driven distributions, bivariate distributions, and number-theoretic distributions. The class is designed to be flexible and extensible, and this is supported in two ways: (1) a function pointer is provided so that the user-programmer can specify an arbitrary probability density function, and (2) new distributions can be easily added by coding them directly into the class. The format of the report is designed to provide the practitioner of Monte Carlo simulations with a handy reference for generating statistical distributions. However, to be self-contained, various techniques for generating distributions are also discussed, as well as procedures for estimating distribution parameters from data. Since most of these distributions rely upon a good underlying uniform distribution of random numbers, several candidate generators are presented along with selection criteria and test results. Indeed, it is noted that one of the more popular generators is probably overused and under what conditions it should be avoided.