ABSTRACT The generalized extreme value distribution, generalized Pareto distribution, Pareto type-I distribution, Pareto type-II distribution, Burr distribution, log-logistic distribution, Fréchet distribution, log-normal distribution, log-Cauchy distribution, Lévy distribution, and Dagum distribution are fitted to four data-sets consisting of surface-level ozone for Weaverville, California (WVR); Tundra Lab, Niwot Ridge, Colorado (TUN); South Pole, Antarctica (SPO); and Mauna Loa, Hawaii (MLO) sites in the USA. Based on the probability distribution with the smallest Akaike information criterion, Bayesian information criterion, corrected Akaike information criterion, mean square error, mean absolute deviation, and maximum deviation values and probability-probability plots, the Dagum distribution emerged as the best fitting distribution for Weaverville, the Burr distribution emerged as the best fitting distribution for Niwot Ridge and Mauna Loa, and the log-Cauchy distribution emerged as the best fitting distribution for the South Pole site. The value at risk for each of the ozone sites is given and a backtest based on the Kupiec test is used to verify the appropriateness of the selected distributions.

中文翻译：

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美国选定地点的地表臭氧灵活重尾分布

摘要 广义极值分布、广义帕累托分布、帕累托 I 型分布、帕累托 II 型分布、Burr 分布、log-logistic 分布、Fréchet 分布、对数正态分布、log-Cauchy 分布、Lévy 分布和 Dagum 分布拟合四个数据集，包括加利福尼亚州韦弗维尔 (WVR) 的地表臭氧；科罗拉多州尼沃特岭的苔原实验室 (TUN)；南极，南极（SPO）；和美国的夏威夷莫纳罗亚 (MLO) 站点。基于具有最小 Akaike 信息准则、贝叶斯信息准则、校正 Akaike 信息准则、均方误差、平均绝对偏差和最大偏差值的概率分布和概率-概率图，Dagum 分布成为 Weaverville 的最佳拟合分布，Burr 分布成为 Niwot Ridge 和 Mauna Loa 的最佳拟合分布，log-Cauchy 分布成为南极站点的最佳拟合分布。给出了每个臭氧站点的风险值，并使用基于 Kupiec 测试的回测来验证所选分布的适当性。