Bernoulli factory: The 2𝚙-coin problem

Hu Shenggang (), Zhang Bo (), Dai Hongsheng () and Liang Wei ()
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Hu Shenggang: Department of Statistics, University of Warwick, Coventry, CV4 7AL, United Kingdom
Zhang Bo: Department of Industrial Engineering, Tsinghua University, Beijing, 100084, P. R. China
Dai Hongsheng: School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
Liang Wei: School of Mathematical Sciences, Xiamen University, Xiamen, 361005, United Kingdom

Monte Carlo Methods and Applications, 2024, vol. 30, issue 4, 365-374

Abstract: This paper aims to address the Bernoulli factory problem of 2 ⁢ p 2\mathtt{p} coins by analysing the relationship between the negative binomial distributions and binomial distributions generated on the same chain of coin flips. The proposed algorithm requires fewer conditions on the constructed sequences compared with the existing algorithms. The feasibility of obtaining such 2 ⁢ p 2\mathtt{p} -coin based on 𝚙-coins will be considered as well.

Keywords: Bernoulli factory; incomplete beta function; negative binomial distribution; Stirling’s approximation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1515/mcma-2024-2016

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