Probabilities of large deviations in the case of stable limit distributions (Q800023)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Probabilities of large deviations in the case of stable limit distributions |
scientific article; zbMATH DE number 3876300
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Probabilities of large deviations in the case of stable limit distributions |
scientific article; zbMATH DE number 3876300 |
Statements
Probabilities of large deviations in the case of stable limit distributions (English)
0 references
1984
0 references
For independent random variables with common distribution function F from the domain of attraction of a stable law and with some special properties the equality \[ P(\sum^{n}_{j=1}X_ j\geq x)=nP(X_ 1\geq x)(1+o(1)) \] is valid uniformly with respect to x in some domain. This domain is described in terms of F. The result generalizes those of V. M. Zolotarev, L. V. Kim and A. V. Nagaev.
0 references
domain of attraction
0 references
stable law
0 references
