IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v13y2007i3p219-225n3.html
   My bibliography  Save this article

Integral Evaluation Using the Δ2-distribution. Simulation and Illustration

Author

Listed:
  • Missov Trifon I.

    (Email:)

Abstract

The Δ2-distribution is a multivariate distribution, which plays an important role in variance reduction of Monte Carlo integral evaluation. Selecting the nodes of random cubature formulae according to Δ2 ensures an unbiased and efficient estimate of the studied integral regardless of the region it is solved over. The Δ2 distribution is also relevant in problems such as separating errors in regression analysis and constructing D-optimal designs in multidimensional regions. Inefficient simulation of Δ2 prevented the application of the underlying theory in real problems. Ermakov and Missov [S.M. Ermakov and T.I. Missov, On Simulation of the Δ2-distribution. Vestnik St. Petersburg University, issue 4 (2005), 123–140.], proposed an algorithm which combines all rejection, inversion, and mixture techniques. Its complexity allows simulating Δ2 vectors of big lengths. Moreover, it works in the most general settings of the problem of integral evaluation. This article presents a modification of the simulation algorithm as well as its illustration for a popular integral in Reliability Theory.

Suggested Citation

  • Missov Trifon I., 2007. "Integral Evaluation Using the Δ2-distribution. Simulation and Illustration," Monte Carlo Methods and Applications, De Gruyter, vol. 13(3), pages 219-225, August.
    • Handle: RePEc:bpj:mcmeap:v:13:y:2007:i:3:p:219-225:n:3
    DOI: 10.1515/mcma.2007.011
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma.2007.011
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma.2007.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    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:bpj:mcmeap:v:13:y:2007:i:3:p:219-225:n:3. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.