论文标题
使用四参数Kappa发行为$ r $ $ - 最大的订单统计数据对气候极端进行建模
Modeling climate extremes using the four-parameter kappa distribution for $r$-largest order statistics
论文作者
论文摘要
使用统计分配对T年度气候极端的T年度回报水平进行准确估算是预测未来气候和工程设计的关键步骤。我们展示了如何通过拟合{四参数kappa分布的$ r $ $ - 最大订单统计}（RK4D）来改进此类数量的估计，这是在本研究中开发的。 RK4D是{$ r $最大的订单统计信息}（RGEVD）的{广义极值分布的扩展，类似于四参数Kappa分布（K4D），这是广义极值分布（GEVD）的扩展。当GEVD中的三个参数不足以捕获极端观测的可变性时，而且还可以通过使用R最大的极端观测值而不是仅仅在降低估计不确定性时，不仅可以捕获数据的可变性，而且还可以捕获估计不确定性，而不仅仅是使用R最大的极端观测值，而不仅仅是块最大值，则此新分布（RK4D）不仅对拟合数据有用。我们得出RK4D的联合概率密度函数（PDF）以及边缘和条件累积分布函数和PDF。为了估计参数，考虑了最大似然估计和最大惩罚可能性估计方法。 RK4D的有用性和实际有效性通过蒙特卡洛模拟以及曼谷极端降雨数据的应用来说明。 $ r $ - 最大的订单统计信息的一些新分布也被推导为RK4D的特殊情况，例如$ r $ - 最大的logistic，$ r $ - 最大的通用逻辑和$ r $ $ $ $ $ r $ - 最大的通用gumbel分布。这些针对$ r $ $的订单统计数据的分布对于为许多研究领域（包括水文学和气候学）建模非常有用。
Accurate estimation of the T-year return levels of climate extremes using statistical distribution is a critical step in the projection of future climate and in engineering design for disaster response. We show how the estimation of such quantities can be improved by fitting {the four-parameter kappa distribution for $r$-largest order statistics} (rK4D), which was developed in this study. The rK4D is an extension of {the generalized extreme value distribution for $r$-largest order statistics} (rGEVD), similar to the four-parameter kappa distribution (K4D), which is an extension of the generalized extreme value distribution (GEVD). This new distribution (rK4D) can be useful not only for fitting data when three parameters in the GEVD are not sufficient to capture the variability of the extreme observations, but also in reducing the estimation uncertainty by making use of the r-largest extreme observations instead of only the block maxima. We derive a joint probability density function (PDF) of rK4D and the marginal and conditional cumulative distribution functions and PDFs. To estimate the parameters, the maximum likelihood estimation and the maximum penalized likelihood estimation methods were considered. The usefulness and practical effectiveness of the rK4D are illustrated by the Monte Carlo simulation and by an application to the Bangkok extreme rainfall data. A few new distributions for $r$-largest order statistics are also derived as special cases of the rK4D, such as the $r$-largest logistic, the $r$-largest generalized logistic, and the $r$-largest generalized Gumbel distributions. These distributions for $r$-largest order statistics would be useful in modeling extreme values for many research areas, including hydrology and climatology.
