Geodesic
Domains of attraction of the max-semistable laws under linear and power normalizations
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 787-799

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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.
Mots-clés : domain of attraction
Keywords: max-stable law, max-semistable law, linear and power normalization. 
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     author = {I. V. Grinevich},
     title = {Domains of attraction of the max-semistable laws under linear and power normalizations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {787--799},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a4/}
}
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I. V. Grinevich. Domains of attraction of the max-semistable laws under linear and power normalizations. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 787-799. http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a4/