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 |
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Pages (from-to) | 1130-1131 |
Journal | Annals of Mathematical Statistics |
Volume | 40 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1969 |
Keywords
- IR-70395