Stability of characterization of a degenerate distribution (Q1097599)
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scientific article; zbMATH DE number 4034846
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of characterization of a degenerate distribution |
scientific article; zbMATH DE number 4034846 |
Statements
Stability of characterization of a degenerate distribution (English)
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1987
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It is evident that if \(F=F^ 2\) and \(F\) is a distribution function, then \(F\) is degenerate. Now let the Lévy distance between the distribution functions \(F\) and \(F^ 2\) not exceed \(\varepsilon\). Then the distance between F and the class of all degenerate distributions does not exceed \(c\varepsilon\ln 1/\varepsilon\), where \(c\) is some absolute constant. The order of this estimate cannot be improved.
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stability of characterization
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Lévy distance
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degenerate distributions
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