A simple proof of Feller's characterization of the compound Poisson distributions (Q1819844)
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scientific article; zbMATH DE number 3994728
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple proof of Feller's characterization of the compound Poisson distributions |
scientific article; zbMATH DE number 3994728 |
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A simple proof of Feller's characterization of the compound Poisson distributions (English)
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1987
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A classical result of \textit{W. Feller} [An introduction to probability theory and its applications. Vol. 1, 3rd ed. (1968; Zbl 0155.231)] is that every distribution that is infinitely divisible and concentrated on the non-negative integers is compound Poisson. We give a simple proof that uses some of the recursive formulas that have recently become popular among actuaries.
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characterization
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Feller's theorem
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infinitely divisible
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compound Poisson
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recursive formulas
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