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Inverting Khintchine’s relationship and generating length biased data

Jones, M. C. (2019). Inverting Khintchine’s relationship and generating length biased data. Statistics & Probability Letters, 154, article no. 108539.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.spl.2019.06.015
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Abstract

If X > 0 follows a distribution with decreasing density, then Khintchine’s theorem states that it has the same distribution as U x S where U and S are independent, following the uniform distribution on (0,1). In this letter, an explicit function of X and independent V ~ U is discovered which has the same distribution as S. This result is then used to find an explicit function of two independent uniform random variables which follows the length biased form of a general distribution on R+ with finite mean.

Item Type: Journal Item
Copyright Holders: 2019 Elsevier
ISSN: 0167-7152
Keywords: Decreasing density; Gibbs sampling; Khintchine’s theorem; Uniform random variables
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 62287
Depositing User: ORO Import
Date Deposited: 03 Jul 2019 12:51
Last Modified: 17 Sep 2019 14:31
URI: http://oro.open.ac.uk/id/eprint/62287
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