Abstract
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.
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