A comparison of L-, LQ-, TL-moment and maximum likelihood high quantile estimates of the GPD and GEV distribution |
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Authors: | Tereza Šimková Jan Picek |
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Affiliation: | Department of Applied Mathematics, Technical University of Liberec, Studentská 1402/2, Liberec, Czech Republic |
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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. |
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Keywords: | Generalized extreme-value distribution Generalized Pareto distribution L-moment LQ-moment TL-moment |
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