Jones, M. C.; Chaubey, Y. P. and Mudholkar, G. S.
Reciprocal symmetry, unimodality and Khintchine's theorem.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2119)
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The symmetric distributions on the real line and their multi-variate extensions play a central role in statistical theory and many of its applications. Furthermore, data in practice often consist of non-negative measurements. Reciprocally symmetric distributions defined on the positive real line may be considered analogous to symmetric distributions on the real line. Hence, it is useful to investigate reciprocal symmetry in general, and Mudholkar and Wang’s notion of R-symmetry in particular. In this paper, we shall explore a number of interesting results and interplays involving reciprocal symmetry, unimodality and Khintchine’s theorem with particular emphasis on R-symmetry. They bear on the important practical analogies between the Gaussian and inverse Gaussian distributions.
||2010 The Royal Society
||Natural Sciences and Engineering Research Council of Canada
||published online before print February 15, 2010
||Cauchy–Schlömilch transformation; Gaussian–inverse Gaussian analogies; Khintchine’s theorem; log-symmetry; R-symmetry; unimodal distributions
||Mathematics, Computing and Technology > Mathematics and Statistics
||28 Dec 2010 22:23
||30 Nov 2012 10:44
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