A characterization of Lévy probability distribution functions on Euclidean spaces

Stephen James Wolfe

Journal of Multivariate Analysis, 1980, vol. 10, issue 3, 379-384

Abstract: In 1937, Paul Lévy proved two theorems that characterize one-dimensional distribution functions of class L. In 1972, Urbanik generalized Lévy's first theorem. In this note, we generalize Lévy's second theorem and obtain a new characterization of Lévy probability distribution functions on Euclidean spaces. This result is used to obtain a new characterization of operator stable distribution functions on Euclidean spaces and to show that symmetric Lévy distribution functions on Euclidean spaces need not be symmetric unimodal.

Keywords: Lévy; probability; distribution; function; operator; stable; distribution; function; characteristic; function; unimodal (search for similar items in EconPapers)
Date: 1980
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(80)90058-5
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:10:y:1980:i:3:p:379-384

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().