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We present new algorithms for computing the exact distributions and p-values of quadratic t-sample distribution-free statistics of Kruskal–Wallis type. These algorithms are presented in terms of generating functions. We show that our algorithm also works for cases with ties and that it is much faster than existing algorithms. Moreover, we show how to use the results for the Kruskal–Wallis type statistics to compute the exact null distribution of the Chacko–Shorack statistic. [Copyright &y& Elsevier]

We present new techniques for computing exact distributions of ‘Friedman-type’ statistics. Representing the null distribution by a generating function allows for the use of general, not necessarily integer-valued rank scores. Moreover, we use symmetry properties of the multivariate generating function to accelerate computations. The methods also work for cases with ties and for permutation statistics. We discuss some applications: the classical Friedman rank test, the normal scores test, the Friedman permutation test, the Cochran–Cox test and the Kepner–Robinson test. Finally, we shortly discuss self-made software for computing exact p-values. [Copyright &y& Elsevier]

In literature, the exact non-null distributions of one and twosample rank statistics are known for small sample sizes (say N ≤ 12) only. To fill the gap between these small sample sizes and sample sizes for which approximations are accurate, new algorithms are developed. These algorithms are based on probability generating functions and we show that they give us the opportunity to compute the exact non-null distribution for much larger samples than the existing algorithms. Finally, we present some applications for nonparametric control charts and power curves. [ABSTRACT FROM AUTHOR]