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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.

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DOI (Digital Object Identifier) Link: http://doi.org/10.1214/08-EJS301
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Abstract

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 Article
ISSN: 1935-7524
Keywords: double symmetry; lognormal distribution; moment equivalence; weighted distribution
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 22528
Depositing User: Sarah Frain
Date Deposited: 18 Aug 2010 13:21
Last Modified: 23 Feb 2016 18:30
URI: http://oro.open.ac.uk/id/eprint/22528
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