On reciprocal symmetry |
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Authors: | MC Jones |
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Institution: | Department of Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK |
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Abstract: | On the positive half line, there are two natural, and complementary, analogues of the single notion of symmetry of distributions on the real line. One is the R-symmetry recently proposed and investigated by Mudholkar and Wang 2007. IG-symmetry and R-symmetry: interrelations and applications to the inverse Gaussian theory. J. Statist. Plann. Inference 137, 3655–3671]; the other is the ‘log-symmetry’ investigated here. Log-symmetry can be thought of either in terms of a random variable having the same distribution as its reciprocal or as ordinary symmetry of the distribution of the logged random variable. Various properties, analogies, comparisons and consequences are investigated. |
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Keywords: | Log-location-scale Log-normal Log-symmetry R-symmetry |
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