An elementary proof of the Knight-Meyer characterization of the Cauchy distribution

Jean-Louis Dunau and Henri Senateur

Journal of Multivariate Analysis, 1987, vol. 22, issue 1, 74-78

Abstract: This paper propounds a short proof of a result previously proved by F. Knight and P. A. Meyer (1976, Z. Warsch. Verw. Gebiete 34 129-134). Let X be a random variable in n with the following property: for any matrix (ca bb) in GL(n+1) (where a is a (n, n) matrix) there exist [alpha] in GL(n) and [beta] in n so that (aX + b)/(cX + d) and ([alpha]X + [beta]) have the same distribution. Then X is necessarily Cauchy distributed.

Keywords: Cauchy; distribution; characterization; type; projective; space (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(87)90076-5
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:22:y:1987:i:1:p:74-78

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 ().