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.

DOI: https://doi.org/10.1016/j.spl.2019.06.015

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.

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About

• Item ORO ID
• 62287
• Item Type
• Journal Item
• ISSN
• 0167-7152
• Keywords
• Decreasing density; Gibbs sampling; Khintchine’s theorem; Uniform random variables
• 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
• © 2019 Elsevier
• Depositing User
• ORO Import