Partial attraction of maxima
Partial attraction of maxima
复制标题
极大值的部分吸引力
DOI：
10.2307/3212678
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发表时间：
1976
影响因子：
1
通讯作者：
R. Green
中科院分区：
文献类型：
--
作者：
R. Green
存在三类对于最大值稳定的概率定律。许多著名的分布都位于这些定律的吸引力范围内。有时通过用稳定法则之一拟合最大值的分布来利用这一事实。然而，这样的过程很可能会被误导，因为存在产生具有任何期望分布而不仅仅是稳定类型的最大值的分布。本文定义了极大值的部分吸引力，并证明了所有分布都具有极大值部分吸引力的非空域。事实上，存在一个分布同时位于所有分布的最大值的部分吸引域中。
There exist three classes of probability laws that are stable for maxima. A number of well-known distributions lie in the domains of attraction of these laws. This fact is sometimes exploited by fitting the distribution of maxima with one of the stable laws. Such a procedure may well be misguided, however, since distributions exist which produce maxima having any desired distribution and not just a stable type. In this paper partial attraction of maxima is defined and it is shown that all distributions have a non-empty domain of partial attraction of maxima. In fact, there exists a distribution that lies simultaneously in the domain of partial attraction of maxima of all distributions.