  By means of a Lynden-Bell integral with deterministic threshold, Worms and
Worms [A Lynden-Bell integral estimator for extremes of randomly truncated
data. Statist. Probab. Lett. 2016; 109: 106-117] recently introduced an
asymptotically normal estimator of the tail index for randomly right-truncated
Pareto-type data. In this context, we consider the random threshold case to
derive a Hill-type estimator and establish its consistency and asymptotic
normality. A simulation study is carried out to evaluate the finite sample
behavior of the proposed estimator.
