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
Date Written: November 08, 2009
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: Suggested Citation