Limit Distributions of Norms of Vectors of Positive i.i.d. Random Variables

Limit Distributions of Norms of Vectors of Positive i.i.d. Random Variables

This paper aims to combine the central limit theorem with the limit theorems in extreme value theory through a parametrized class of limit theorems where the former ones appear as special cases. To this end the limit distributions of suitably centered and normalized lcp(n)-norms of n-vectors of posi...

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Veröffentlicht in:The Annals of Probability. - Institute of Mathematical Statistics. - 29(2001), 2, Seite 862-881
1. Verfasser: Schlather, Martin (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2001
Zugriff auf das übergeordnete Werk:The Annals of Probability
Schlagworte:Central Limit Theorem Extreme Value Theory i.i.d. Positive Random Variables lp-Norm Limit Theorems Normal Distribution Mathematics Applied sciences Philosophy
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520 |a This paper aims to combine the central limit theorem with the limit theorems in extreme value theory through a parametrized class of limit theorems where the former ones appear as special cases. To this end the limit distributions of suitably centered and normalized lcp(n)-norms of n-vectors of positive i.i.d. random variables are investigated. Here, c is a positive constant and p(n) is a sequence of positive numbers that is given intrinsically by the form of the upper tail behavior of the random variables. A family of limit distributions is obtained if c runs over the positive real axis. The normal distribution and the extreme value distributions appear as the endpoints of these families, namely, for c = 0+ and c = ∞, respectively. 
540 |a Copyright 2001 Institute of Mathematical Statistics 
650 4 |a Central Limit Theorem 
650 4 |a Extreme Value Theory 
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650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions 
650 4 |a Applied sciences  |x Computer science  |x Artificial intelligence  |x Machine learning  |x Perceptron convergence procedure 
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