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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

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A bit of context would be nice. (Where did you see this written?) – Willie Wong Feb 10 '11 at 12:32
Sure, see my edit. – tauran Feb 10 '11 at 13:30
up vote 1 down vote accepted

I'm pretty sure $N$ in the context means the size of the set $\Omega$, the total number of images. See beginning of section 3.1 of the linked paper. And in $N.\hat{N}_{fa}(S)$, the $.$ should just be multiplication. So the entire term should be interpreted as a distribution of the number of false alarms (total number times the cumulative distribution).

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Thank you, that sounds reasonable. I guess I was thinking too complicated. Given that it is just a normal multiplication, am I right if I consider this as bad formatting? – tauran Feb 10 '11 at 14:21
@tauran: good and bad formatting is partly subjective (although there are of course guides like the Chicago Manual of Style); that said, I feel that you are quite justified in feeling that way. – Willie Wong Feb 10 '11 at 17:03

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