The Open UniversitySkip to content

Distributions that are both log-symmetric and R-symmetric

Jones, M. C. and Arnold, Barry C. (2008). Distributions that are both log-symmetric and R-symmetric. Electronic Journal of Statistics, 2 pp. 1300–1308.

Full text available as:
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (138kB)
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of logY) and R-symmetry. In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equivalent to the lognormal distribution. They include the lognormal, some members of the Berg/Askey class of distributions, and a number of others for which we give an explicit construction (based on work of A.J. Pakes) and note some properties; Stieltjes classes, however, are not doubly symmetric.

Item Type: Journal Item
ISSN: 1935-7524
Keywords: double symmetry; lognormal distribution; moment equivalence; weighted distribution
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 22528
Depositing User: Sarah Frain
Date Deposited: 18 Aug 2010 13:21
Last Modified: 08 Dec 2018 03:45
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU