  The pseudo-Lindley distribution which was introduced in Zeghdoudi and Nedjar
(2016) is studied with regards to its upper tail. In that regard, and when the
underlying distribution function follows the Pseudo-Lindley law, we investigate
the behavior of its values, the asymptotic normality of the Hill estimator and
the double-indexed generalized Hill statistic process (Ngom and Lo), the
asymptotic normality of the records values and the moment problem.
