On reciprocal symmetry

Jones, M. C. (2008). On reciprocal symmetry. Journal of Statistical Planning and Inference, 138(10) pp. 3039–3043.

DOI: https://doi.org/10.1016/j.jspi.2007.11.006


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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