If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimators
of the tail index of a distribution to data which are rounded off one often observes that
these estimators oscillate strongly as a function of the number k of order statistics
involved.We study this phenomenon in the case of a Pareto distribution. We provide
formulas for the expected value and variance of the Hill estimator and give bounds on
k when the central limit theorem is still applicable. We illustrate the theory by using
simulated and real-life data.