Characterizing the distributions of the random variables \(X_ 1,X_ 2,X_ 3\) by the distribution of \((X_ 1-X_ 3,X_ 2-X_ 3)\) (Q1067682)
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scientific article; zbMATH DE number 3930019
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterizing the distributions of the random variables \(X_ 1,X_ 2,X_ 3\) by the distribution of \((X_ 1-X_ 3,X_ 2-X_ 3)\) |
scientific article; zbMATH DE number 3930019 |
Statements
Characterizing the distributions of the random variables \(X_ 1,X_ 2,X_ 3\) by the distribution of \((X_ 1-X_ 3,X_ 2-X_ 3)\) (English)
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1986
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Let \(X_ 1,X_ 2,X_ 3\) be independent random variables. In this paper we investigate under which conditions the distribution of the random vector \((X_ 1-X_ 3,X_ 2-X_ 3)\) determines the distributions of \(X_ 1,X_ 2,X_ 3\) up to a change of the location. For a class of random variables a necessary and sufficient condition is given.
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change of the location
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0.8168726
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0.8125944
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