Let $F$ be the distribution of a random variable and $f$ be its density. How can we approximate the value of $\int_0^{1} \frac{p(1-p)}{n[f(F^{-1}(p)]} dp$?
Note: $\frac{p(1-p)}{n[f(F^{-1}(p)]}$ is the asymptotic variance of the distribution of order statistics from iid samples with distribution $F$. So we want to get some idea of the variance of order statistics for every $p$.
