A Lynden-Bell integral estimator for the tail index of right-truncated   data with a random threshold
  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. 
Nawel Haouas, Abdelhakim Necir, Djamel Meraghni, Brahim Brahimi
math.ST stat.TH