What does $N.\hat{N}_{fa}(S)$ mean, when $\hat{N}_{fa}(S)$ is a cumulative distribution function? $\hat{N}_{fa}(S) = \sum\limits_{s=0}^{S}\hat{p}_{fa}(s)$
The formula is from this paper (section 4.2): Logo Retrieval with A Contrario Visual Query Expansion