Correcting remarks on "characterization of normality within the class of elliptical contoured distributions"

T. Cacoullos and C. G. Khatri

Statistics & Probability Letters, 1991, vol. 11, issue 6, 551-552

Abstract: Let x have a spherical distribution (SD), with characteristic function [phi](t't), t [epsilon] Tp, to be denoted by x [approximate] Sp([phi]). Let x'Ax be a quadratic form, with A = A'. A correction is given to Theorem 1 in Khatri and Mukerjee (1987), wrongly asserting that if Q = x'Ax is chi-square distributed with r degrees of freedom ([chi]2r), then x is necessarily normal and r = Rank(A), the rank of A. A related characterization of the gamma-type SD (1.1) by a gamma-distributed Q is also given.

Keywords: Spherical; distributions; quadratic; form; [chi]2-characterization; of; normality (search for similar items in EconPapers)
Date: 1991
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(91)90122-8
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:stapro:v:11:y:1991:i:6:p:551-552

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

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().