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...
| Veröffentlicht in: | The Annals of Probability. - Institute of Mathematical Statistics. - 29(2001), 2, Seite 862-881 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2001
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| 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 |
| Zusammenfassung: | 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. |
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| ISSN: | 00911798 |