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A comparison of estimators for the generalised Pareto distribution

Mackay, E.B.L., Challenor, P.G. and Bahaj, A.S. (2011) A comparison of estimators for the generalised Pareto distribution Ocean Engineering, 38, (11-12), pp. 1338-1346. (doi:10.1016/j.oceaneng.2011.06.005).

Record type: Article


The generalised Pareto distribution (GPD) is often used to model the distribution of storm peak wave heights exceeding a high threshold, from which return values can be calculated. There are large differences in the performance of various parameter and quantile estimators for the GPD. Commonly used estimation methods such as maximum likelihood or probability weighted moments are not optimal, especially for smaller sample sizes. The performance of several estimators for the GPD is compared by the Monte Carlo simulation and the implications for estimating return values of significant wave height are discussed. Of the estimators compared, the likelihood-moment (LM) estimator has close to the lowest bias and variance over a wide range of sample sizes and GPD shape parameters. The LM estimator always exists, is simple to compute and has a low sensitivity to choice of threshold. It is recommended that the LM estimator is used for calculating return values of significant wave height when the sample size is less than 500. For sample sizes above 500 the NEW estimator of Zhang and Stephens (2009) can give accurate results for low computational cost.

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Published date: August 2011
Keywords: extremes, peaks-over-threshold, generalised pareto distribution, estimator
Organisations: Marine Systems Modelling, Centre for Environmental Science


Local EPrints ID: 196103
ISSN: 0029-8018
PURE UUID: 8b57eff5-c7d6-49c7-bd41-69d97e75c5e8
ORCID for A.S. Bahaj: ORCID iD

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Date deposited: 02 Sep 2011 13:52
Last modified: 18 Jul 2017 11:23

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