 Sensitivity curve

Add one observation $z$ to the empirical sample, so $F_{n+1,z}=\frac{n}{n+1}{F}_n+\frac{1}{n+1}{\delta }_z$. The displayed finite difference is a finite-sample counterpart of the influence function. Its supremum magnitude measures worst-case one-observation sensitivity; unlike an infinitesimal derivative it records the actual response at contamination fraction $1/(n+1)$.