Note on Completely Monotone Densities

F.W. Sleutel

doi:10.1214/aoms/1177697626

Note on Completely Monotone Densities

F.W. Sleutel

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Abstract

In [2] it is proved that mixtures of exponential distributions are infinitely divisible (id). In [3] it is proved that the same holds for the discrete analogue, i.e. for mixtures of geometric distributions. In this note we show that these results imply that a density function $f(x)$ (or distribution $\{p_n\}$ on the integers) is id if the function $f(x)$ (or the sequence $\{p_n\}$ is completely monotone (cm). For the definition and properties of cm functions and sequences we refer to [1].

Original language	English
Pages (from-to)	1130-1131
Journal	Annals of Mathematical Statistics
Volume	40
Issue number	3
DOIs	https://doi.org/10.1214/aoms/1177697626
Publication status	Published - 1969

Keywords

IR-70395

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Sleutel, F. W. (1969). Note on Completely Monotone Densities. Annals of Mathematical Statistics, 40(3), 1130-1131. https://doi.org/10.1214/aoms/1177697626

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