Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1130-1131 |
| Journal | Annals of Mathematical Statistics |
| Volume | 40 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1969 |
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Keywords
- IR-70395
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Note on Completely Monotone Densities. / Sleutel, F.W.
In: Annals of Mathematical Statistics, Vol. 40, No. 3, 1969, p. 1130-1131.Research output: Contribution to journal › Article › Academic
TY - JOUR
T1 - Note on Completely Monotone Densities
AU - Sleutel, F.W.
PY - 1969
Y1 - 1969
N2 - 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].
AB - 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].
KW - IR-70395
U2 - 10.1214/aoms/1177697626
DO - 10.1214/aoms/1177697626
M3 - Article
VL - 40
SP - 1130
EP - 1131
JO - Annals of Mathematical Statistics
JF - Annals of Mathematical Statistics
SN - 0003-4851
IS - 3
ER -