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Reciprocal symmetry, unimodality and Khintchine's theorem

Jones, M. C.; Chaubey, Y. P. and Mudholkar, G. S. (2010). Reciprocal symmetry, unimodality and Khintchine's theorem. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2119) pp. 2097–2116.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1098/rspa.2009.0636
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Abstract

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.

Item Type: Journal Article
Copyright Holders: 2010 The Royal Society
ISSN: 1364-5021
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetNatural Sciences and Engineering Research Council of Canada
Extra Information: published online before print February 15, 2010
Keywords: Cauchy–Schlömilch transformation; Gaussian–inverse Gaussian analogies; Khintchine’s theorem; log-symmetry; R-symmetry; unimodal distributions
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 25816
Depositing User: Sarah Frain
Date Deposited: 28 Dec 2010 22:23
Last Modified: 30 Nov 2012 10:44
URI: http://oro.open.ac.uk/id/eprint/25816
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