# Characterizations of discrete compound Poisson distributions

*Huiming Zhang* and
*Bo Li*

*Communications in Statistics - Theory and Methods*, 2016, vol. 45, issue 22, 6789-6802

**Abstract:**
The aim of this paper is to give some new characterizations of discrete compound Poisson distributions. Firstly, we give a characterization by the Lévy–Khintchine formula of infinitely divisible distributions under some conditions. The second characterization need to present by row sum of random triangular arrays converges in distribution. And we give an application in probabilistic number theory, the strongly additive function converging to a discrete compound Poisson in distribution. The next characterization, is an extension of Watanabe’s theorem of characterization of homogeneous Poisson process. The last characterization will be illustrated by waiting time distributions, especially the matrix-exponential representation.

**Date:** 2016

**References:** Add references at CitEc

**Citations:** View citations in EconPapers (1) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1080/03610926.2014.901375 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:taf:lstaxx:v:45:y:2016:i:22:p:6789-6802

**Ordering information:** This journal article can be ordered from

http://www.tandfonline.com/pricing/journal/lsta20

**DOI:** 10.1080/03610926.2014.901375

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by *Debbie Iscoe*

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals

Bibliographic data for series maintained by Chris Longhurst ().