Mathematical Sciences: Random Variables and Computers

这项研究的主要目标是开发为特定机器量身定制的随机数生成器，以及在各种机器中产生完全相同结果的通用随机数生成器；为随机数生成器开发测试，以评估其是否适合复杂用途和庞大的样本量，现在已变得司空见惯；以及开发新的或改进的方法来生成蒙特卡罗研究中使用的重要随机变量。本研究计划的另一个目标是提供新的或更好的方法来评估计算统计中的重要分布函数，如正态分布和不完全分布。科学计算可分为两部分：确定性计算和蒙特卡罗计算。后者需要在计算的各个阶段随机输入。这个研究项目集中在科学计算的那一方面：在蒙特卡罗计算中随机变量的生成、测试和使用。

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.