Positive definite symmetric functions on finite dimensional spaces. I. Applications of the Radon transform

Donald St. P. Richards

Journal of Multivariate Analysis, 1986, vol. 19, issue 2, 280-298

Abstract: An n-dimensional random vector X is said (Cambanis, S., Keener, R., and Simons, G. (1983). J. Multivar. Anal., 13 213-233) to have an [alpha]-symmetric distribution, [alpha] > 0, if its characteristic function is of the form [phi]([xi]1[alpha] + ... + [xi]n[alpha]). Using the Radon transform, integral representations are obtained for the density functions of certain absolutely continuous [alpha]-symmetric distributions. Series expansions are obtained for a class of apparently new special functions which are encountered during this study. The Radon transform is also applied to obtain the densities of certain radially symmetric stable distributions on n. A new class of "zonally" symmetric stable laws on n is defined, and series expansions are derived for their characteristic functions and densities.

Keywords: positive; definite; [alpha]-symmetric; finite; dimension; Radon; transform; Gegenbauer; polynomial; stable; distribution; density; functions; Bessel; function (search for similar items in EconPapers)
Date: 1986
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(86)90033-3
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:19:y:1986:i:2:p:280-298

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 ().