Abstract

In this article, we characterize the classes of absolutelycontinuous distributions concentrated on $(0, \infty)$ anddiscrete distributions concentrated on $\{0,1,2, ...\}$, with(non-vanishing survivor functions having) completely monotonehazard functions; in the latter case, we refer to the hazardfunctions also as the hazard sequences. These provide us withcharacterizations of the certain specialized versions of mixturesof exponential and geometric distributions with mixingdistributions, satisfying some further criteria, which by theGoldie-Steutel theorem and  a result of Kaluza are seen to bespecialized versions of infinitely divisible distributions. Weshed light on the implications of our findings, giving somepertinent examples and remarks.

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