Note on Completely Monotone Densities

F.W. Sleutel

    Research output: Contribution to journalArticleAcademic

    22 Downloads (Pure)

    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 languageEnglish
    Pages (from-to)1130-1131
    JournalAnnals of Mathematical Statistics
    Volume40
    Issue number3
    DOIs
    Publication statusPublished - 1969

    Keywords

    • IR-70395

    Fingerprint Dive into the research topics of 'Note on Completely Monotone Densities'. Together they form a unique fingerprint.

  • Cite this