Asymptotics of the shorth plot

The shorth plot is a nonparametric method to visualize probability mass concentration. It is based on the length of the shortest interval containing a certain fraction of the probability distribution and a point x. We establish functional central limit theorems (convergence rate 1 / n ) for the empirical shorth plot under natural conditions. The limiting process is not necessarily Gaussian. In the proofs, we generalize the Vervaat (1972) lemma to a collection of functions.