The combination of Mathematica's high algebraic capacity and method of generating functions is becoming an extremely efficient tool in probability theory and statistics. After an introductory example and a short overview on nonparametric methods, we show how generating functions of discrete statistics can be handled using Mathematica. Next, we solve two combinatorial problems, which are essential in calculating the generating function of nonparametric test statistics. Finally, these methods are used to produce accurate and extensive tables and plots of the distributions of some of the most popular nonparametric test statistics. Furthermore, we use graphs to illustrate approximations of the distributions of these test statistics by standard distributions.
An Introductory Example
Two Combinatorial Problems
The Wilcoxon Rank Sum Test
The Kruskal-Wallis Analysis of Variance
Back to our Introductory Example
About the Author
Peter Weiß studied mathematics at the University of Innsbruck. Since 1973 he has been a professor for probability and mathematical statistics at the Johannes Kepler University in Linz. His current areas of interest are point-processes, random walk on random structures, and statistical data analysis for industrial applications. In 1990 he founded the new curriculum "Mechatronics," which is a combination of mechanical engineering, electrical engineering, and computer science.
Institute of Mathematics
Johannes Kepler University