Inverting Khintchine’s relationship and generating length biased data

M.C. Jones

Statistics & Probability Letters, 2019, vol. 154, issue C, -

Abstract: If X>0 follows a distribution with decreasing density, then Khintchine’s theorem states that it has the same distribution as U×S where U and S>0 are independent, U following the uniform distribution on (0,1). In this letter, an explicit function of X and independent V∼U(0,1) 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.

Keywords: Decreasing density; Gibbs sampling; Khintchine’s theorem; Uniform random variables (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.06.015

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