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Bernoulli factory: The 2𝚙-coin problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hu Shenggang & Zhang Bo & Dai Hongsheng & Liang Wei, 2024. "Bernoulli factory: The 2𝚙-coin problem," Monte Carlo Methods and Applications, De Gruyter, vol. 30(4), pages 365-374.
    • Handle: RePEc:bpj:mcmeap:v:30:y:2024:i:4:p:365-374:n:1003
    DOI: 10.1515/mcma-2024-2016
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