Distributions that are both log-symmetric and R-symmetric

M. C. Jones; Barry C. Arnold

doi:10.1214/08-ejs301

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arXiv · 0810.0102

Distributions that are both log-symmetric and R-symmetric

M. C. Jones·Barry C. Arnold

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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 $\log Y$) 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. 2008-12-22. Distributions that are both log-symmetric and R-symmetric. https://doi.org/10.1214/08-ejs301

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