The main goal of this research is the development of random number generators tailored for particular machines as well as universal ones that produce exactly the same results in a variety of machines; the development of tests for random number generators that assess their suitability for the sophisticated uses and huge sample sizes now becoming commonplace; and the development of new or improved methods for generating the important random variables used in Monte Carlo studies. Another goal of this research program is to provide new or better methods for evaluating the important distribution functions in computational statistics, such as the normal and the incomplete gamma and beta distributions. Scientific computation may be divided into two parts: deterministic and Monte Carlo. The latter requires random inputs at various stages of the computations. This research program concentrates on that aspect of scientific computation: the generation, testing and use of random variables in Monte Carlo calculations.
