title: The exact probability distribution of the rank product statistics for replicated experiments.
abstract: 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.
authors: Department of Social Science Research Methods, Radboud University Nijmegen, Netherlands. r.eisinga@maw.ru.nl
authors: Rob
authors: R
authors: Eisinga
authors: Rainer
authors: R
authors: Breitling
authors: Tom
authors: T
authors: Heskes
mesh_terms: D000465:Algorithms; D030541:Databases, Genetic; D020869:Gene Expression Profiling / Q000706:statistics & numerical data*; D006801:Humans; D007938:Leukemia / Q000235:genetics*; D008957:Models, Genetic; D009363:Neoplasm Proteins / Q000235:genetics*; D020411:Oligonucleotide Array Sequence Analysis / Q000706:statistics & numerical data*; D011336:Probability
chemical_list: D009363:Neoplasm Proteins