Does false discovery rate estimate some population quantity? False discovery rate (FDR) is defined as

FDR = FP / (TP + FP).

Does it estimate some population quantity, independent of sample, when the sample satisfies some condition?
To make it clearer, True positive rate is defined as 

TPR = TP/ (TP + FN)

If all the points in the sample come from a sample distribution $F$ in the alternative hypothesis, true positive rate estimates $P_{X \sim F}($ reject null $)$.     
 A: The FDR of an inference procedure cannot estimate any quantity, as it is, by itself, a fixed quantity. Think of it as a generalization of the type I error-- which you would never call "an estimate".
One can however, estimate the FDR of a given inference procedure. Try [1] as a starting reference.
[1] Storey, John D. "A direct approach to false discovery rates." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64.3 (2002): 479-498.
A: Efron and Tibshirani's new book Computer Age Statistical Inference offers an intuitive understanding to what is being estimated. Let me summarize their message graphically.
The (Bayesian) underlying idea is that observations come from a mixture of two distributions:


*

*$\pi_0 \: N$ observations from the null density $f_0(z)$

*$(1-\pi_0) \: N$ observations from alternative density $f_1(z)$.


What is observed is the mixture of those two:


*

*$f(z) = \pi_0 \cdot f_0(z) + (1-\pi_0) \cdot f_1(z)$



The (Bayesian) definitions are:


*

*$\text{Fdr} = \frac{\pi_0 \: (1-F_0(z_0))}{(1-F(z))}$  (a fraction of the tail areas)

*$\text{fdr} = \frac{\pi_0 \: f_0(z_0)}{f(z)}$  (a fraction of the tail densities)


As shown below, Fdr is equivalent to the Benjamini hocherg FDR when $\pi_0 \approx 1$ (which is the case in most bioinformatics studies)

