论文标题
系列计划中的极端指数及其应用
Extremal Indices in the Series Scheme and their Applications
论文作者
论文摘要
我们将固定随机序列的极端指数的概念推广到相同分布的随机变量的串联方案，其随机串联大小的概率趋向于无穷大。我们通过两个定义概括了经典极好指数的基本属性，从而介绍了新的极端指数。我们证明了新的极端指数的一些有用属性。我们展示了如何根据新的极端指数来描述骨料活动最大值（在信息网络模型中）（在信息网络模型中）（在信息网络模型中）的行为（在信息网络模型中）以及随机粒子得分的最大值（在生物种群模型中）。我们还获得了具有Copulas和阈值模型的模型的新结果。我们表明，新索引可以为同一系统采用不同的值，以及大于一个的值。
We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices through two definitions generalizing the basic properties of the classical extremal index. We prove some useful properties of the new extremal indices. We show how the behavior of aggregate activity maxima on random graphs (in information network models) and the behavior of maxima of random particle scores in branching processes (in biological population models) can be described in terms of the new extremal indices. We also obtain new results on models with copulas and threshold models. We show that the new indices can take different values for the same system, as well as values greater than one.
