Exact calculation of false discovery rate for step-up and step-down procedures

We derive exact formulas for the false discovery rate (FDR) and the Power of any step-up and step-down procedures and for the $s$-th moment of the false discovery proportion (FDP) of any step-up procedure. These formulas are "explicit" in the sense that they only involve the parameters of the model and elementary operations. The $p$-values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true/false hypotheses is used. We propose several applications of theses formulas. In particular, some new results related to least/most favorable configurations for the FDR and the variance of the FDP are presented.