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The cumulative distribution and quantile functions for the one-sided onesample Kolmogorov-Smirnov probability distributions are used forgoodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDFappears straight forward, its numerical evaluation generates intermediateresults spanning many hundreds of orders of magnitude and at times requiresvery precise accurate representations. Computing the quantile function for anyspecific probability may require evaluating both the CDF and its derivative,both of which are computationally expensive. To work around avoid these issues,different algorithms can be used across different parts of the domain, andapproximations can be used to reduce the computational requirements. We showhere that straight forward implementation incurs accuracy loss for sample sizesof well under 1000. Further the approximations in use inside the open sourceSciPy python software often result in increased computation, not just reducedaccuracy, and at times suffer catastrophic loss of accuracy for any samplesize. Then we provide alternate algorithms which restore accuracy andefficiency across the whole domain.

Computing the Cumulative Distribution Function and Quantiles of the One-sided Kolmogorov-Smirnov Statistic