An algorithm for computing the exact distribution of the Wilcoxon signed-rank statistic

In this paper, we propose an efficient algorithm to compute the exact distribution of the Wilcoxon signed-rank test. The proposed algorithm is straightforward and easy to program even if ranks are tied and is efficient to compute the probability mass function. A simulation study was performed to compare the exact distribution and the normal approximation. We also compared computing times of the proposed method with those of other methods. We present the R program in which the core contents of the proposed algorithm are written.