Gumbel极值value distribution推广应用于风速资料的比较评论
A comparative review of generalizations of the Gumbel extreme value distribution with an application to wind speed data
摘要：
广义极值分布及其特例Gumbel极值分布在极值分析中有着广泛的应用。Gumbel分布有一定的缺点，因为它是一个非重尾分布，其特征是恒定的偏度和峰度。广义极值分布经常在这种情况下使用，因为它包含了三种可能的极限分布，用于独立和同分布观测的无限样本的归一化最大值。然而，广义极值分布可能不是一个合适的模型时，每个观察到的最大值不是来自大量的观察。因此，Gumbel分布的其他形式的推广可能是更可取的。我们的目标是收集在目前的文献中的分布，包含Gumbel分布嵌入其中，并确定那些具有灵活的偏度和峰度，重尾，并可能与广义极值分布的竞争。广义的Gumbel分布的描述和比较使用的应用程序的风速数据集和蒙特卡罗模拟。我们发现，一些分布遭受过参数化，并与其他广义Gumbel分布与较少的参数，即，是不可识别的。我们的研究表明，在实际应用中应考虑广义极值分布和两个极值分布的混合。
英文摘要：
The generalized extreme value distribution and its particular case, the Gumbel extreme value distribution, are widely applied for extreme value analysis. The Gumbel distribution has certain drawbacks because it is a non-heavy-tailed distribution and is characterized by constant skewness and kurtosis. The generalized extreme value distribution is frequently used in this context because it encompasses the three possible limiting distributions for a normalized maximum of infinite samples of independent and identically distributed observations. However, the generalized extreme value distribution might not be a suitable model when each observed maximum does not come from a large number of observations. Hence, other forms of generalizations of the Gumbel distribution might be preferable. Our goal is to collect in the present literature the distributions that contain the Gumbel distribution embedded in them and to identify those that have flexible skewness and kurtosis, are heavy-tailed and could be competitive with the generalized extreme value distribution. The generalizations of the Gumbel distribution are described and compared using an application to a wind speed data set and Monte Carlo simulations. We show that some distributions suffer from overparameterization and coincide with other generalized Gumbel distributions with a smaller number of parameters, i.e., are non-identifiable. Our study suggests that the generalized extreme value distribution and a mixture of two extreme value distributions should be considered in practical applications.
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