Tail fitting for truncated and non-truncated Pareto-type distributions
Tail fitting for truncated and non-truncated Pareto-type distributions
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DOI：
10.1007/s10687-016-0247-3
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发表时间：
2016-09-01
期刊：
影响因子：
1.3
通讯作者：
Gomes, Ivette
中科院分区：
文献类型：
--
作者：
Beirlant, Jan;Alves, Isabel Fraga;Gomes, Ivette
在极值分析中，自然的上限可能会出现，截断概率尾部。在其他情况下，最终在最大的数据，偏离帕累托尾行为变得明显。当需要在样本之外进行外推时，这一点尤其重要。考虑到在实际中人们并不总是知道分布是否被截断，我们考虑截断和非截断Pareto型分布下的极值分位数的估计。我们利用截断帕累托分布的尾部指数的估计，首先在Aban等人（J. Amer. Statistist. 101（473），270-277，2006）。我们还提出了一个截断的帕累托QQ图和截断的正式测试，以帮助决定截断和非截断的情况。通过这种方式，我们扩大了使用帕累托尾的极值建模的可能性，通过添加相对于可用数据较大的截断点T来提供替代方案。因此，在数学建模中，与极值估计中使用的数据的限制分数（k/n -> 0）相比，我们让T -> 8处于不同的速度。这项工作的动机是使用来自不同领域的实际例子，仿真结果，和一些渐近结果。
In extreme value analysis, natural upper bounds can appear that truncate the probability tail. At other instances ultimately at the largest data, deviations from a Pareto tail behaviour become apparent. This matter is especially important when extrapolation outside the sample is required. Given that in practice one does not always know whether the distribution is truncated or not, we consider estimators for extreme quantiles both under truncated and non-truncated Pareto-type distributions. We make use of the estimator of the tail index for the truncated Pareto distribution first proposed in Aban et al. (J. Amer. Statist. Assoc. 101(473), 270-277, 2006). We also propose a truncated Pareto QQ-plot and a formal test for truncation in order to help deciding between a truncated and a non-truncated case. In this way we enlarge the possibilities of extreme value modelling using Pareto tails, offering an alternative scenario by adding a truncation point T that is large with respect to the available data. In the mathematical modelling we hence let T -> 8 at different speeds compared to the limiting fraction (k/n -> 0) of data used in the extreme value estimation. This work is motivated using practical examples from different fields, simulation results, and some asymptotic results.