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A comparison of estimators for the generalised Pareto distribution

A comparison of estimators for the generalised Pareto distribution
A comparison of estimators for the generalised Pareto distribution
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.
extremes, peaks-over-threshold, generalised pareto distribution, estimator
0029-8018
1338-1346
Mackay, E.B.L.
01c96888-d032-42ff-b601-eef96269c4ad
Challenor, P.G.
a7e71e56-8391-442c-b140-6e4b90c33547
Bahaj, A.S.
a64074cc-2b6e-43df-adac-a8437e7f1b37
Mackay, E.B.L.
01c96888-d032-42ff-b601-eef96269c4ad
Challenor, P.G.
a7e71e56-8391-442c-b140-6e4b90c33547
Bahaj, A.S.
a64074cc-2b6e-43df-adac-a8437e7f1b37

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), 1338-1346. (doi:10.1016/j.oceaneng.2011.06.005).

Record type: Article

Abstract

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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More information

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

Identifiers

Local EPrints ID: 196103
URI: http://eprints.soton.ac.uk/id/eprint/196103
ISSN: 0029-8018
PURE UUID: 8b57eff5-c7d6-49c7-bd41-69d97e75c5e8
ORCID for A.S. Bahaj: ORCID iD orcid.org/0000-0002-0043-6045

Catalogue record

Date deposited: 02 Sep 2011 13:52
Last modified: 15 Mar 2024 02:32

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Contributors

Author: E.B.L. Mackay
Author: P.G. Challenor
Author: A.S. Bahaj ORCID iD

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