| It is known that there are six types of power stable laws for the limit distribu-tions of maxima under power normalization as its limit distribution is nondegenerate. A lot of researches have been done related to limit distributions of maxima under power normalization. The importance is obvious to study the necessary and suffi-cient conditions for a given distribution belonging to one type of power normalized extreme value distributions.The content of thesis is about a given distribution function belongs to one class of the p-max stable laws under Von Mises conditions, which includes two main parts. The first part mainly focuses on sufficient conditions for a distribution function under power normalization, and each sufficient condition corresponds to a tail representation of the given distribution function. In the second part, a kind of restricted domain of attraction is discussed under power normalization, and the necessary and sufficient conditions of six classes of domain of attraction are obtained. |
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