The Estimation of Parameters for the Tapered Pareto Distribution from Incomplete Data

In this paper, we consider estimation of unknown parameters of the tapered Pareto distribution, which belongs to the class of semiheavy distributions, by a sample with excluded ℓ n largest and k n smallest observations. We establish necessary and sufficient conditions in terms of proportions k n /n and ℓ n /n for weak consistency and joint asymptotic normality of parameterizedmoment-type estimators for the shape and form parameters. Additionally, we extend the result on weak consistency of generalized Hill statistics (introduced in [V. Paulauskas and M. Vaičiulis, On the improvement of Hill and some others estimators, Lith. Math. J. , 53(3):336–355, 2013]) to the case where the extreme value index is not positive. We demonstrate the performance of the proposed estimators on both simulated data from the tapered Pareto distribution and real data from finance.