Topic
Infinite divisibility
About: Infinite divisibility is a research topic. Over the lifetime, 611 publications have been published within this topic receiving 11178 citations.
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TL;DR: In this paper, analogues for the concepts of self-decomposability and stability for distributions on the nonnegative integers were proposed, and it turns out that these "discrete self-Decomposable" and "Discrete Stable" distributions have properties that are quite similar to those of their continuous counterparts.
Abstract: Analogues are proposed for the concepts of self-decomposability and stability for distributions on the nonnegative integers. It turns out that these "discrete self-decomposable" and "discrete stable" distributions have properties that are quite similar to those of their continuous counterparts.
701 citations
Book•
03 Oct 2003
TL;DR: In this paper, the authors present a list of well-known distributions notations and conventions, as well as prerequisites from probability and analysis list of distributions notation and conventions for stochastic processes.
Abstract: infinitely divisible distributions on the nonnegative integers infinitely divisible distributions on the nonnegative reals infinitely divisible distributions on the real line self-decomposability and stability infinite divisibility and mixtures infinite divisibility in stochastic processes. Appendices: prerequisites from probability and analysis list of well-known distributions notations and conventions.
488 citations
TL;DR: New inequalities for the gamma and psi functions are presented, and new classes of completely monotonic, star-shaped, and superadditive functions which are related to Γ and?
Abstract: We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, star-shaped, and superadditive functions which are related to Γ and?.
429 citations
TL;DR: In this article, the class of subexponential distribution functions with Levy measure v was studied and the following assertions were proved: 1) For F infinitely divisible on [0, ∞] with Levy measures v, the following results on ∞ are established.
Abstract: Let ℒ denote the class of subexponential distribution functions. For F infinitely divisible on [0, ∞) with Levy measure v, the following assertions are proved to be equivalent:
In the proof of this theorem, some new results on ∞ are established.
330 citations
318 citations