Indexing metadata

Some New Approaches to Infinite Divisibility


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Some New Approaches to Infinite Divisibility
 
2. Creator Author's name, affiliation, country Theofanis Sapatinas; University of Cyprus; Cyprus
 
2. Creator Author's name, affiliation, country Damodar Shanbhag; University of Cyprus; Cyprus
 
2. Creator Author's name, affiliation, country Arjun K Gupta; Bowling Green State University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Kaluza sequences; Infinite divisibility; Log-convexity; Mixtures of exponential distributions; Mixtures of geometric distributions; Wiener-Hopf factorization
 
3. Subject Subject classification 60E05
 
4. Description Abstract Using an approach based, amongst other things, on Proposition 1 of Kaluza (1928), Goldie (1967) and, using a different approach based especially on zeros of polynomials, Steutel (1967) have proved that each nondegenerate distribution function (d.f.) $F$ (on $\mathbb{R}$, the real line), satisfying $F(0-)=0$ and $F(x)=F(0)+(1-F(0))G(x), x > 0$, where $G$ is the d.f. corresponding to a mixture of exponential distributions, is infinitely divisible. Indeed, Proposition 1 of Kaluza (1928) implies that any nondegenerate discrete probability distribution $\{p_x:x=0,1,\ldots\}$ that is log-convex or, in particular, completely monotone, is compound geometric, and, hence, infinitely divisible. Steutel (1970), Shanbhag & Sreehari (1977) and Steutel & van Harn (2004, Chapter VI) have given certain extensions or variations of one or more of these results. Following a modified version of the C.R. Rao et al. (2009, Section 4) approach based on the Wiener-Hopf factorization, we establish some further results of significance to the literature on infinite divisibility.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2011-11-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/961
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-961
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.