IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i9p2097-d1135556.html
   My bibliography  Save this article

Antithetic Power Transformation in Monte Carlo Simulation: Correcting Hidden Errors in the Response Variable

Author

Listed:
  • Dennis Ridley

    (School of Business & Industry, Florida A&M University, Tallahassee, FL 32307, USA
    Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA)

  • Pierre Ngnepieba

    (Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, USA)

Abstract

Monte Carlo simulation is performed with uniformly distributed U(0,1) pseudo-random numbers. Because the numbers are generated from a mathematical formula, they will contain some serial correlation, even if very small. This serial correlation becomes embedded in the correlation structure of the response variable. The response variable becomes an asynchronous time series. This leads to hidden errors in the response variable. The purpose of this paper is to illustrate how this happens and how it can be corrected. The method is demonstrated for the case of a simple queue for which the time in the system is known exactly from theory. The paper derives the correlation between an exponential random variable and its antithetic counterpart obtained by power transform with an infinitesimal negative exponent.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2097-:d:1135556
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/9/2097/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/9/2097/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dennis Ridley & Pierre Ngnepieba, 2014. "Antithetic time series analysis and the CompanyX data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 83-94, January.
    2. Jack P. C. Kleijnen, 1975. "Antithetic Variates, Common Random Numbers and Optimal Computer Time Allocation in Simulation," Management Science, INFORMS, vol. 21(10), pages 1176-1185, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Elena Almaraz Luengo & Carlos Gragera, 2023. "Critical Analysis of Beta Random Variable Generation Methods," Mathematics, MDPI, vol. 11(24), pages 1-31, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dag Kolsrud, 2008. "Stochastic Ceteris Paribus Simulations," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 21-43, February.
    2. Dennis Ridley & Pierre Ngnepieba, 2014. "Antithetic time series analysis and the CompanyX data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 83-94, January.
    3. Kleijnen, J.P.C., 1978. "The role of statistical methodology in simulation," Other publications TiSEM 05085a08-4669-4775-adc5-4, Tilburg University, School of Economics and Management.
    4. Shing Chih Tsai & Chen Hao Kuo, 2012. "Screening and selection procedures with control variates and correlation induction techniques," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 340-361, August.
    5. Kleijnen, J.P.C., 1997. "Experimental Design for Sensitivity Analysis, Optimization and Validation of Simulation Models," Discussion Paper 1997-52, Tilburg University, Center for Economic Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2097-:d:1135556. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.