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Modelling Dry Spells by Extreme Value Distribution with Bayesian Inference

机译：用贝叶斯推理的极值分布模拟干法术

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摘要

Two theoretically justified models of extremes are applied to dry spell (DS) series: the generalized Pareto distribution is applied to peak-over-threshold data (POT-GP), and the generalized extreme value distribution is applied to the annual maxima (AM-GEV). DS data are categorized according to three precipitation-per-day limits (1, 5 and 10mm). The inference on the corresponding parameters is evaluated within the Bayesian paradigm, where the fact that DS values are recorded discretely as a whole number of days (forming the rounded series) can be incorporated in a straightforward manner. The study confirmed precautionary estimations when applying the GEV model on annual maxima in comparison with a simpler Gumbel model. Regarding the POT-GP modelling, the Bayesian approach reveals a high uncertainty that can occur in parameter estimations when very high thresholds are considered. It is found that there are no clear criteria in the assessment of some optimal threshold, nor is there a necessity for its detection. Instead, Bayesian inference provides a reasonable overall picture of the range of thresholds compatible with the GP model. Furthermore, it is suggested that all three GP parameters should be assessed when using the rounded data. The location estimates should be compatible with the theoretical value of -0.5. Although the present study was performed mainly on DS series from two stations in Croatia spanning the period 1961-2015, the methodology developed here should be applicable to other regions.
机译：两个理论上的极端模型适用于干法术（DS）系列：广义帕累托分布应用于峰值过阈值数据（POT-GP），并且广泛的极值分布应用于年度最大值（AM- GEV）。 DS数据根据三个每日三次降水限制（1,5和10mm）进行分类。在贝叶斯范式内评估对应参数的推断，其中DS值在离散地作为整个天数（形成圆形系列）的事实可以以直接的方式结合。该研究确认了与简单的Gumbel模型相比，在年度最大值上应用GEV模型时的预防估计。关于POT-GP建模，贝叶斯方法揭示了在考虑非常高阈值时可以在参数估计中发生的高不确定性。结果发现，对一些最佳阈值的评估没有明确的标准，也没有必要进行检测。相反，贝叶斯推理提供了与GP模型兼容的阈值范围的合理整体画面。此外，建议在使用舍入数据时应该评估所有三个GP参数。位置估计应与理论值兼容-0.5。虽然本研究主要是在跨越1961 - 2015年克罗地亚的两个站点的DS系列上进行，但这里开发的方法应该适用于其他地区。

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