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2008 Distributions that are both log-symmetric and R-symmetric
M.C. Jones, Barry C. Arnold
Electron. J. Statist. 2: 1300-1308 (2008). DOI: 10.1214/08-EJS301


Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of logY) and R-symmetry [7]. 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.


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M.C. Jones. Barry C. Arnold. "Distributions that are both log-symmetric and R-symmetric." Electron. J. Statist. 2 1300 - 1308, 2008.


Published: 2008
First available in Project Euclid: 22 December 2008

zbMATH: 1320.62026
MathSciNet: MR2471288
Digital Object Identifier: 10.1214/08-EJS301

Primary: 62E10
Secondary: 60E05

Keywords: double symmetry , Lognormal distribution , moment equivalence , weighted distribution

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society


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