Decomposition of Exponential Distributions on Positive Semigroups

Kyle Siegrist ()
Additional contact information
Kyle Siegrist: University of Alabama in Huntsville

Journal of Theoretical Probability, 2006, vol. 19, issue 1, 204-220

Abstract: Let (S,·) be a positive semigroup and T a sub-semigroup of S. In many natural cases, an element $$x\in S$$ can be factored uniquely as x=yz, where $$y \in T$$ and where z is in an associated “quotient space” S/T. If X has an exponential distribution on S, we show that Y and Z are independent and that Y has an exponential distribution on T. We prove a converse when the sub-semigroup is $$S_t =\{t^n : n \in\mathbb{N}\}$$ for $$t\in S$$ . Specifically, we show that if Y t and Z t are independent and Y t has an exponential distribution on S t for each $$t\in S$$ , then X has an exponential distribution on S. When applied to ([0,∞), +) and $$(\mathbb{N}, +)$$ , these results unify and extend known results on the quotient and remainder when X is divided by t.

Keywords: Positive semigroup; exponential distribution; geometric distribution; sub-semigroup; quotient space (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-006-0005-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:19:y:2006:i:1:d:10.1007_s10959-006-0005-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-006-0005-6

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().