标题： 关于分布函数在最大稳定定律吸引域中的熵收敛性 显示英文标题

标题： On convergence of entropy of distribution functions in the max domain of attraction of max stable laws

摘要： 最大稳定律是独立同分布（iid）随机变量的线性标准化部分极大值的极限律，它们类似于归一化部分和的极限稳定律。本文研究了在线性标准化下，最大稳定律吸引域中的分布函数的熵极限定理。更具体地说，我们研究了当线性标准化的部分极大值收敛到某个非退化随机变量时，独立同分布随机变量的线性标准化部分极大值的香农熵收敛到相应极限熵的问题。我们能够证明，在某些情况下，香农熵不仅收敛，而且实际上会增加到极限熵。我们讨论了多个例子。我们还研究了与第k个上极端值相关的类似结果。 显示英文摘要

摘要： Max stable laws are limit laws of linearly normalized partial maxima of indepen- dent, identically distributed (iid) random variables (rvs). These are analogous to stable laws which are limit laws of normalized partial sums of iid rvs. In this paper, we study entropy limit theorems for distribution functions in the max domain of attraction of max stable laws under linear normalization. More specifically, we study the problem of convergence of the Shannon entropy of linearly normalized partial maxima of iid rvs to the corresponding limit entropy when the linearly normalized partial maxima converges to some nondegenerate rv. We are able to show that the Shannon entropy not only converges but, in fact, increases to the limit entropy in some cases. We discuss several examples. We also study analogous results for the k-th upper extremes.