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June, 1969 Note on Completely Monotone Densities
F. W. Steutel
Ann. Math. Statist. 40(3): 1130-1131 (June, 1969). DOI: 10.1214/aoms/1177697626


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].


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F. W. Steutel. "Note on Completely Monotone Densities." Ann. Math. Statist. 40 (3) 1130 - 1131, June, 1969.


Published: June, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0183.47601
MathSciNet: MR254949
Digital Object Identifier: 10.1214/aoms/1177697626

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 3 • June, 1969
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