Une caractérisation des lois exponentielles et géométriques. (A characterization of the exponential and geometric laws) (Q913394)
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scientific article; zbMATH DE number 4147285
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Une caractérisation des lois exponentielles et géométriques. (A characterization of the exponential and geometric laws) |
scientific article; zbMATH DE number 4147285 |
Statements
Une caractérisation des lois exponentielles et géométriques. (A characterization of the exponential and geometric laws) (English)
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1989
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Given a probability law \(\mu\) on (0,\(\infty)\) (resp. \({\mathbb{N}}^*)\), we give a necessary and sufficient condition \(\mu\) to be the exponential (resp. geometric) probability law. This condition is expressed by a proportionality relation between the average number of jumps of the counting process associated with \(\mu\) in a certain random time interval and the average length of this interval.
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characterization
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exponential distribution
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geometric distribution
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proportionality relation
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average number of jumps
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counting process
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