Pitfalls in Using Weibull Tailed Distributions

Journal of Statistical Planning and Inference, 2010, Volume 140, Issue 7, p.2018- 2024

11 Pages Posted: 11 Sep 2013

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Deyuan Li

Fudan University

Liang Peng

Georgia Institute of Technology

Date Written: November 08, 2009

Abstract

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of this drawback, a Weibull tailed distribution has been studied recently.

Some methods for choosing the sample fraction in estimating the Weibull tail coefficient and some bias reduction estimators have been proposed in the literature. In this paper, we show that the theoretical optimal sample fraction does not exist and a bias reduction estimator does not always produce a smaller mean squared error than a biased estimator. These are different from using a heavy tailed distribution. Further we propose a refined class of Weibull tailed distributions which are more useful in estimating high quantiles and extreme tail probabilities.

Keywords: Asymptotic Mean Squared Error, Extreme Tail Probability, High Quantile, Regular Variation, Weibull Tail Coefficient

JEL Classification: C10, C60

Suggested Citation

Asimit, Alexandru Vali and Li, Deyuan and Peng, Liang, Pitfalls in Using Weibull Tailed Distributions (November 08, 2009). Journal of Statistical Planning and Inference, 2010, Volume 140, Issue 7, p.2018- 2024. Available at SSRN: https://ssrn.com/abstract=2323520

Alexandru Vali Asimit

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Deyuan Li (Contact Author)

Fudan University ( email )

Beijing West District Baiyun Load 10th
Shanghai, 100045
China

Liang Peng

Georgia Institute of Technology ( email )

Atlanta, GA 30332
United States

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