SetTest

It provides cumulative distribution function (CDF), quantile, p-value, statistical power calculator and random number generator for a collection of group-testing procedures, including the Higher Criticism tests, the one-sided Kolmogorov-Smirnov tests, the one-sided Berk-Jones tests, the one-sided phi-divergence tests, etc. The input are a group of p-values. The null hypothesis is that they are i.i.d. Uniform(0,1). In the context of signal detection, the null hypothesis means no signals. In the context of the goodness-of-fit testing, which contrasts a group of i.i.d. random variables to a given continuous distribution, the input p-values can be obtained by the CDF transformation. The null hypothesis means that these random variables follow the given distribution. For reference, see [1]Hong Zhang, Jiashun Jin and Zheyang Wu. "Distributions and power of optimal signal-detection statistics in finite case", IEEE Transactions on Signal Processing (2020) 68, 1021-1033; [2] Hong Zhang and Zheyang Wu. "The general goodness-of-fit tests for correlated data", Computational Statistics & Data Analysis (2022) 167, 107379.

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