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Critical Analysis of Beta Random Variable Generation Methods

Author

Listed:
  • Elena Almaraz Luengo

    (Department of Statistics and Operational Research, Faculty of Mathematical Science, Complutense University of Madrid, 28040 Madrid, Spain)

  • Carlos Gragera

    (Faculty of Mathematical Science, Complutense University of Madrid, 28040 Madrid, Spain)

Abstract

The fast generation of values of the beta random variable is a subject of great interest and multiple applications, ranging from purely mathematical and statistical ones to applications in management and production, among others. There are several methods for generating these values, with one of the essential points for their design being the selection of random seeds. Two interesting aspects converge here: the use of sequences as inputs (and the need for them to verify properties such as randomness and uniformity, which are verified through statistical test suites) and the design of the algorithm for the generation of the variable. In this paper, we analyse, in detail, the algorithms that have been developed in the literature, both from a mathematical/statistical and computational point of view. We also provide empirical development using R software, which is currently in high demand and is one of the main novelties with respect to previous comparisons carried out in FORTRAN. We establish which algorithms are more efficient and in which contexts, depending on the different values of the parameters, allowing the user to determine the best method given the experimental conditions.

Suggested Citation

  • Elena Almaraz Luengo & Carlos Gragera, 2023. "Critical Analysis of Beta Random Variable Generation Methods," Mathematics, MDPI, vol. 11(24), pages 1-31, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4893-:d:1295312
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    References listed on IDEAS

    as
    1. Ovidiu Bagdasar & Minsi Chen & Vasile Drăgan & Ivan Ganchev Ivanov & Ioan-Lucian Popa, 2023. "On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators," Mathematics, MDPI, vol. 11(5), pages 1-16, March.
    2. Bruce W. Schmeiser, 1980. "Technical Note—Generation of Variates from Distribution Tails," Operations Research, INFORMS, vol. 28(4), pages 1012-1017, August.
    3. Dennis Ridley & Pierre Ngnepieba, 2023. "Antithetic Power Transformation in Monte Carlo Simulation: Correcting Hidden Errors in the Response Variable," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    4. James E. Kelley, 1961. "Critical-Path Planning and Scheduling: Mathematical Basis," Operations Research, INFORMS, vol. 9(3), pages 296-320, June.
    5. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption," Mathematics, MDPI, vol. 11(14), pages 1-23, July.
    6. D. G. Malcolm & J. H. Roseboom & C. E. Clark & W. Fazar, 1959. "Application of a Technique for Research and Development Program Evaluation," Operations Research, INFORMS, vol. 7(5), pages 646-669, October.
    7. Bruce W. Schmeiser & A. J. G. Babu, 1980. "Beta Variate Generation via Exponential Majorizing Functions," Operations Research, INFORMS, vol. 28(4), pages 917-926, August.
    Full references (including those not matched with items on IDEAS)

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