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The exact probability distribution of the rank product statistics for replicated experiments
Author(s) -
Eisinga Rob,
Breitling Rainer,
Heskes Tom
Publication year - 2013
Publication title -
febs letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.593
H-Index - 257
eISSN - 1873-3468
pISSN - 0014-5793
DOI - 10.1016/j.febslet.2013.01.037
Subject(s) - statistic , permutation (music) , mathematics , statistics , rank (graph theory) , product (mathematics) , distribution (mathematics) , sampling (signal processing) , sampling distribution , combinatorics , computer science , mathematical analysis , physics , geometry , filter (signal processing) , acoustics , computer vision
The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities.