A comparison of L-, LQ-, TL-moment and maximum likelihood high quantile estimates of the GPD and GEV distribution

ABSTRACT

In this article, L-moments, LQ-moments and TL-moments of the generalized Pareto and generalized extreme-value distributions are derived up to the fourth order. The first three L-, LQ- and TL-moments are used to obtain estimators of their parameters. Performing a simulation study, high-quantile estimates based on L-, LQ-, and TL-moments are compared to the maximum likelihood estimate with respect to their sample mean squared error. This consists of identifying an optimal combination of parameters α and p both considered in the range [0, 0.5] for estimating quantiles by LQ-moments. The results show L-moment and maximum likelihood methods outperform other methods.

KEYWORDS:

• Generalized extreme-value distribution
• Generalized Pareto distribution
• L-moment
• LQ-moment
• TL-moment

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10

Acknowledgments

This work has been supported by the Czech Science Foundation under project 14-18675S and by the Student Grant Competition under project 21116 on the Faculty of Science, Humanities and Education, Technical University of Liberec. The author thanks the referee for the comments, which helped to better understanding the text.