Advanced science and technology provide a wealth of big data from different sources for extreme value analysis. Classical 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 consistency and asymptotic normality are obtained for the maximum likelihood estimation of the parameters involved in the accelerated p-max and p-min stable distributions when it exists. 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：先进科学技术为极值分析提供了来自不同来源的丰富大数据。经典极值理论已被扩展，以获得一个加速最大稳定分布族，用于建模基于竞争风险的极端数据（Cao and Zhang, 2021）。本文为来自竞争风险的幂正态化最大值与最小值建立了概率模型。其极限分布包含一个扩展的、新的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。对于加速p-最大和p-最小稳定分布中存在的参数，我们获得了其最大似然估计的一致性与渐近正态性。极限分布类型主要由样本生成过程及竞争风险之间的相互作用决定，这通过常见示例加以说明。此外，本文研究了关于该模型的最大似然估计与模型诊断的统计推断。数值研究首先展示了所有极限场景的有效逼近，以及与线性正态化下相比具有可比性的收敛速率，随后呈现了针对模拟数据集的加速p-最大/p-最小稳定模型的最大似然估计与诊断。最后，关于地面臭氧年最大值和斯坦福心脏移植存活时间的两个真实数据集，展示了我们的加速p-最大和加速p-最小稳定模型的性能。