Expected difference of order statistics in terms of hazard rate
Boris Tsirelson·2019-11-16·via math.PR updates on arXiv.org
If the hazard rate $ \frac{ F'(x) }{ 1-F(x) } $ is increasing (in $x$), then $ \mathbb E\, ( X_{n:n} - X_{n-1:n} ) $ is decreasing (in $n$), and moreover, completely monotone.