Stability of a characterization of normal distributions based on the first two conditional moments (Q1578361)
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scientific article; zbMATH DE number 1496726
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of a characterization of normal distributions based on the first two conditional moments |
scientific article; zbMATH DE number 1496726 |
Statements
Stability of a characterization of normal distributions based on the first two conditional moments (English)
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19 September 2000
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A characterization of normal distributions of two independent random variables \(X\) and \(Y\) with a finite \(E[X^2]\) based on the linearity of \(E[X \mid X+Y]\) and the homoscedasticity of \(\text{var} [X\mid X+Y]\) given by \textit{C.R. Rao} [Ann. Stat. 4, 823-835 (1976; Zbl 0341.62029)] is proved to be stable.
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conditional density function
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normal close
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characteristic function
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small parameter
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