  It was shown that when one disposes of a parametric information of the
truncation distribution, the semiparametric estimator of the distribution
function for truncated data (Wang, 1989) is more efficient than the
nonparametric one. On the basis of this estimation method, we derive an
estimator for the tail index of Pareto-type distributions that are randomly
right-truncated and establish its consistency and asymptotic normality. The
finite sample behavior of the proposed estimator is carried out by simulation
study. We point out that, in terms of both bias and root of the mean squared
error, our estimator performs better than those based on nonparametric
estimation methods. An application to a real dataset of induction times of AIDS
diseases is given as well.
