Note on Completely Monotone Densities

F.W. Sleutel

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    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 languageEnglish
    Pages (from-to)1130-1131
    JournalAnnals of Mathematical Statistics
    Issue number3
    Publication statusPublished - 1969


    • IR-70395


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