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Questioning MLE for the estimation of environmental extreme distributions

机译：质疑MLE以估计环境极端分布

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摘要

In determining extreme environmental variables, such as wave heights, with the Peaks-Over-Threshold (POT) method, it has become common practice in the metocean community to use the GPD-Poisson model fitted by the Maximum Likelihood Estimator (MLE). However, Mazas and Hamm (2011) pointed out some difficulties in getting stable estimations of extreme quantiles with this method. Further investigation reported in the present paper enable to understand that this problem is linked to the behavior of the likelihood function and to solve it by introducing a location parameter and replacing maximum likelihood estimated two-parameter distributions by L-moments estimated three-parameter distributions. Applications on real and simulated data highlight the distinction between the location parameter of a statistical distribution and the statistical threshold chosen in the POT context. With three-parameter distributions, MLE is no more suitable and it is found that the L-moments estimator can be a valid alternative. With these two improvements, stable quantiles are obtained not only with the GPD but also with other distributions such as Weibull and Gamma (Pearson-Ⅲ).
机译：在使用波峰阈值（POT）方法确定极端环境变量（例如波高）时，使用最大似然估计器（MLE）拟合的GPD-泊松模型已成为海洋社会的惯例。但是，Mazas和Hamm（2011）指出了使用这种方法获得极端分位数的稳定估计的一些困难。本文中报道的进一步研究能够理解此问题与似然函数的行为有关，并通过引入位置参数并将最大似然估计的两参数分布替换为L矩估计的三参数分布来解决此问题。对真实数据和模拟数据的应用突出了统计分布的位置参数和在POT上下文中选择的统计阈值之间的区别。对于三参数分布，MLE不再合适，并且发现L矩估计量可以作为有效的替代方案。通过这两个改进，不仅可以使用GPD获得稳定的分位数，而且还可以使用其他分布（例如Weibull和Gamma（Pearson-Ⅲ））获得稳定的分位数。

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