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On an intriguing distributional identity

Jones, M. C.; Marchand, E. and Strawderman, W. E. (2018). On an intriguing distributional identity. The American Statistician, 73(1) pp. 16–21.

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For a continuous random variable X with support equal to (a, b), with c.d.f. F, and g: Ω1 → Ω2 a continuous, strictly increasing function, such that Ω1∩Ω2⊇(a, b), but otherwise arbitrary, we establish that the random variables F(X) − F(g(X)) and F(g−1(X)) − F(X) have the same distribution. Further developments, accompanied by illustrations and observations, address as well the equidistribution identity U − ψ(U) = dψ−1(U) − U for UU(0, 1), where ψ is a continuous, strictly increasing and onto function, but otherwise arbitrary. Finally, we expand on applications with connections to variance reduction techniques, the discrepancy between distributions, and a risk identity in predictive density estimation.

Item Type: Journal Item
Copyright Holders: 2019 American Statistical Association
ISSN: 0003-1305
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetNatural Sciences and Engineering Research Council of Canada
Not Set209035Simons Foundation
Not Set418098Simons Foundation
Keywords: Equidistribution; Identity; Uniform distribution
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 50722
Depositing User: M. C. Jones
Date Deposited: 29 Aug 2017 13:33
Last Modified: 03 May 2019 00:29
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