Domains of Attraction of the Max-Semistable Laws under Linear and Power Normalizations
Domains of Attraction of the Max-Semistable Laws under Linear and Power Normalizations
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线性和幂归一化下最大半稳定定律的吸引力域
DOI：
10.1137/1138064
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
I. V. Grinevigh
中科院分区：
文献类型：
--
作者：
I. V. Grinevigh
本文研究了独立同分布随机变量累积极大值方案中一元半稳定律的吸引域，得到了在线性和幂正规化下非退化分布函数属于极大半稳定律吸引域的充要条件.这些定理包括著名的标准属于域的吸引力的最大稳定的法律作为一种特殊情况下，例子。在线性和功率归一化的吸引域之间的关系示出。
We consider the domains of attraction of the univariate semi-stable laws in the scheme of cumulative maxima of independent identically distributed random variables and obtain necessary and sufficient conditions for a nondegenerate distribution function to belong to the domain of attraction of a max-semistable law under linear and power normalization. These theorems include the well-known criteria for belonging to the domains of attraction of max-stable laws as a special case; examples are given. The relation between the domains of attraction under linear and power normalization is shown.