Advanced science and technology provide a wealth of big data from different sources for extreme value analysis.Classic extreme value theory was extended to obtain an accelerated max-stable distribution family for modelling competing risk-based extreme data in Cao and Zhang (2021). In this paper, we establish probability models for power normalized maxima and minima from competing risks. The limit distributions consist of an extensional new accelerated max-stable and min-stable distribution family (termed as the accelerated p-max/p-min stable distribution), and its left-truncated version. The limit types of distributions are determined principally by the sample generating process and the interplay among the competing risks, which are illustrated by common examples. Further, the statistical inference concerning the maximum likelihood estimation and model diagnosis of this model was investigated. Numerical studies show first the efficient approximation of all limit scenarios as well as its comparable convergence rate in contrast with those under linear normalization, and then present the maximum likelihood estimation and diagnosis of accelerated p-max/p-min stable models for simulated data sets. Finally, two real datasets concerning annual maximum of ground level ozone and survival times of Stanford heart plant demonstrate the performance of our accelerated p-max and accelerated p-min stable models.

翻译：先进科技为极值分析提供了大量来自不同来源的大数据。经典极值理论被扩展，以获得用于建模基于竞争风险的极端数据的加速最大稳定分布族（Cao and Zhang, 2021）。本文建立了竞争风险下幂标准化极大值与极小值的概率模型。极限分布包括一个扩展的新加速最大稳定与最小稳定分布族（称为加速p-最大/p-最小稳定分布）及其左截断版本。极限分布类型主要由样本生成过程及竞争风险间的相互作用决定，并通过常见示例加以说明。进一步研究了该模型的最大似然估计与模型诊断的统计推断。数值研究表明，所有极限场景的近似效率以及其与线性标准化下收敛速度相当，随后展示了模拟数据集下加速p-最大/p-最小稳定模型的最大似然估计与诊断。最后，两个关于地面臭氧年最大值与斯坦福心脏移植患者生存时间的真实数据集，展示了我们加速p-最大与加速p-最小稳定模型的性能。