Statistical models for overdispersion in the frequency of peaks over threshold data for a flow series
Statistical models for overdispersion in the frequency of peaks over threshold data for a flow series
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DOI：
10.1029/2009wr007757
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发表时间：
2010-02
影响因子：
5.4
通讯作者：
E. Eastoe;J. Tawn
中科院分区：
文献类型：
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作者：
E. Eastoe;J. Tawn
在一系列河流流量的峰值超阈值分析中，使用一个足够高的阈值来提取独立洪水事件的峰值。本文回顾了现有的这类事件的年度统计模型，并提出了新的统计模型。现有的最常见的事件时间过程模型是齐次泊松过程。这个模型是由渐近理论驱动的。然而，经验证据表明，这不是最合适的模型，因为它意味着年度计数的平均值和方差是相同的，而计数似乎是过度分散的，即方差大于平均值。本文描述了齐次泊松过程如何被扩展以包括事件发生速率中的时间变化，从而通过使用回归和混合模型来帮助解释年度计数中的过度分散。文中还讨论了这些新模型对年极大值隐含概率分布的影响。这些模型是用泰晤士河在金斯敦的历史流量系列来说明的。
In a peaks over threshold analysis of a series of river flows, a sufficiently high threshold is used to extract the peaks of independent flood events. This paper reviews existing, and proposes new, statistical models for both the annual counts of such events and the process of event peak times. The most common existing model for the process of event times is a homogeneous Poisson process. This model is motivated by asymptotic theory. However, empirical evidence suggests that it is not the most appropriate model, since it implies that the mean and variance of the annual counts are the same, whereas the counts appear to be overdispersed, i.e., have a larger variance than mean. This paper describes how the homogeneous Poisson process can be extended to incorporate time variation in the rate at which events occur and so help to account for overdispersion in annual counts through the use of regression and mixed models. The implications of these new models on the implied probability distribution of the annual maxima are also discussed. The models are illustrated using a historical flow series from the River Thames at Kingston.