### 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

### Cite this

*Annals of Mathematical Statistics*,

*40*(3), 1130-1131. https://doi.org/10.1214/aoms/1177697626

}

*Annals of Mathematical Statistics*, vol. 40, no. 3, pp. 1130-1131. https://doi.org/10.1214/aoms/1177697626

**Note on Completely Monotone Densities.** / Sleutel, F.W.

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 -