Note on Completely Monotone Densities
Steutel, F. W.
Ann. Math. Statist., Tome 40 (1969) no. 6, p. 1130-1131 / Harvested from Project Euclid
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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].
Publié le : 1969-06-14
Classification:  
@article{1177697626,
     author = {Steutel, F. W.},
     title = {Note on Completely Monotone Densities},
     journal = {Ann. Math. Statist.},
     volume = {40},
     number = {6},
     year = {1969},
     pages = { 1130-1131},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177697626}
}

Steutel, F. W. Note on Completely Monotone Densities. Ann. Math. Statist., Tome 40 (1969) no. 6, pp.  1130-1131. http://gdmltest.u-ga.fr/item/1177697626/