Reciprocal symmetry, unimodality and Khintchine's theorem

Chaubey, Yogendra P.; Mudholkar, Govind S. and Jones, M. C. (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: https://doi.org/10.1098/rspa.2009.0482

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.

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About

• Item ORO ID
• 25816
• Item Type
• Journal Item
• ISSN
• 1364-5021
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	Natural Sciences and Engineering Research Council of Canada

• Keywords
• Cauchy–Schlömilch transformation; Gaussian–inverse Gaussian analogies; Khintchine’s theorem; log-symmetry; R-symmetry; unimodal distributions
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2010 The Royal Society
• Depositing User
• Sarah Frain