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Mendo Tomas, LuisAuthor

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December 10, 2024
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Simulating a coin with irrational bias using rational arithmetic

Publicated to:Communications In Statistics-Simulation And Computation. 54 (1): 302-318 - 2025-01-02 54(1), DOI: 10.1080/03610918.2024.2425702

Authors: Mendo, L

Affiliations

Univ Politecn Madrid, Madrid, Spain - Author

Abstract

An algorithm is presented that, taking independent Bernoulli random variables with parameter 1/2 as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter tau. It requires a series representation of tau with positive, rational terms, and a rational bound on its truncation error that converges to 0. The number of required inputs has an exponentially bounded tail, and its mean is at most 3. The number of arithmetic operations has a tail that can be bounded in terms of the sequence of truncation error bounds. The algorithm is applied to two specific values of tau, including Euler's constant, for which obtaining a simple simulation algorithm was an open problem.

Keywords

65c1065c50Bernoulli random variablesConsensus algorithmIndependent bernoulli random variablesMsc201Msc2010Random number generationRandom variablesRandom-number generationRational arithmeticRational arithmeticsSeriesSimulationTruncation errors

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Communications In Statistics-Simulation And Computation due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2025, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Modeling and Simulation. Notably, the journal is positioned en el Cuartil Q3 for the agency WoS (JCR) in the category Statistics & Probability.

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-09-19:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 2.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 13.2.
  • The number of mentions on the social network X (formerly Twitter): 7 (Altmetric).

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (Manrique, Daniel).

the author responsible for correspondence tasks has been Manrique, Daniel.