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Extended generalised Pareto models for tail estimation

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Extended generalised Pareto models for tail estimation. / Papastathopoulos, Ioannis; Tawn, Jonathan Angus.
In: Journal of Statistical Planning and Inference, Vol. 143, No. 1, 01.2013, p. 131-143.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Papastathopoulos, I & Tawn, JA 2013, 'Extended generalised Pareto models for tail estimation', Journal of Statistical Planning and Inference, vol. 143, no. 1, pp. 131-143. https://doi.org/10.1016/j.jspi.2012.07.001

APA

Papastathopoulos, I., & Tawn, J. A. (2013). Extended generalised Pareto models for tail estimation. Journal of Statistical Planning and Inference, 143(1), 131-143. https://doi.org/10.1016/j.jspi.2012.07.001

Vancouver

Papastathopoulos I, Tawn JA. Extended generalised Pareto models for tail estimation. Journal of Statistical Planning and Inference. 2013 Jan;143(1):131-143. Epub 2012 Jul 7. doi: 10.1016/j.jspi.2012.07.001

Author

Papastathopoulos, Ioannis ; Tawn, Jonathan Angus. / Extended generalised Pareto models for tail estimation. In: Journal of Statistical Planning and Inference. 2013 ; Vol. 143, No. 1. pp. 131-143.

Bibtex

@article{ade92e4fbcce4241bf9fad483b5f6aee,
title = "Extended generalised Pareto models for tail estimation",
abstract = "The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the model fits the data well. Sometimes, few observations of a measurement process might be recorded in applications and so selecting a high quantile of the sample as the threshold leads to almost no exceedances. In this paper we propose extensions of the generalised Pareto distribution that incorporate an additional shape parameter while keeping the tail behaviour unaffected. The inclusion of this parameter offers additional structure for the main body of the distribution, improves the stability of the modified scale, tail index and return level estimates to threshold choice and allows a lower threshold to be selected. We illustrate the benefits of the proposed models with a simulation study and two case studies.",
keywords = "Extreme value theory, Extended generalised Pareto distribution, Tail estimation, Threshold selection, Liver toxicity",
author = "Ioannis Papastathopoulos and Tawn, {Jonathan Angus}",
year = "2013",
month = jan,
doi = "10.1016/j.jspi.2012.07.001",
language = "English",
volume = "143",
pages = "131--143",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Extended generalised Pareto models for tail estimation

AU - Papastathopoulos, Ioannis

AU - Tawn, Jonathan Angus

PY - 2013/1

Y1 - 2013/1

N2 - The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the model fits the data well. Sometimes, few observations of a measurement process might be recorded in applications and so selecting a high quantile of the sample as the threshold leads to almost no exceedances. In this paper we propose extensions of the generalised Pareto distribution that incorporate an additional shape parameter while keeping the tail behaviour unaffected. The inclusion of this parameter offers additional structure for the main body of the distribution, improves the stability of the modified scale, tail index and return level estimates to threshold choice and allows a lower threshold to be selected. We illustrate the benefits of the proposed models with a simulation study and two case studies.

AB - The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the model fits the data well. Sometimes, few observations of a measurement process might be recorded in applications and so selecting a high quantile of the sample as the threshold leads to almost no exceedances. In this paper we propose extensions of the generalised Pareto distribution that incorporate an additional shape parameter while keeping the tail behaviour unaffected. The inclusion of this parameter offers additional structure for the main body of the distribution, improves the stability of the modified scale, tail index and return level estimates to threshold choice and allows a lower threshold to be selected. We illustrate the benefits of the proposed models with a simulation study and two case studies.

KW - Extreme value theory

KW - Extended generalised Pareto distribution

KW - Tail estimation

KW - Threshold selection

KW - Liver toxicity

U2 - 10.1016/j.jspi.2012.07.001

DO - 10.1016/j.jspi.2012.07.001

M3 - Journal article

VL - 143

SP - 131

EP - 143

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1

ER -