首页> 外文期刊>Journal of statistical computation and simulation >A comparative review of generalizations of the Gumbel extreme value distribution with an application to wind speed data
【24h】

A comparative review of generalizations of the Gumbel extreme value distribution with an application to wind speed data

机译:Gumbel极值分布的概括性比较研究及其在风速数据中的应用

获取原文
获取原文并翻译 | 示例

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, that is, 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.
机译:广义极值分布及其特殊情况Gumbel极值分布被广泛应用于极值分析。 Gumbel分布具有某些缺点,因为它是非重尾分布,并且具有恒定的偏斜度和峰度特征。广义极值分布在这种情况下经常使用,因为它包含独立和相同分布观测值的无限大样本的归一化最大值的三种可能的极限分布。但是,当每个观察到的最大值都不来自大量观察值时,广义极值分布可能不是合适的模型。因此,Gumbel分布的其他形式的概括可能是更可取的。我们的目标是在当前文献中收集包含嵌入其中的Gumbel分布的分布,并确定具有灵活偏斜度和峰度,重尾且可以与广义极值分布竞争的分布。使用风速数据集的应用程序和蒙特卡洛模拟对Gumbel分布的一般性进行了描述和比较。我们表明,某些分布遭受过度参数化的影响,并且与参数数量较少(即无法识别)的其他广义Gumbel分布一致。我们的研究表明,在实际应用中应考虑广义的极值分布和两种极值分布的混合。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号