IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0118537.html

Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space

Author

Listed:
  • Bin Wang
  • Wenzhong Shi
  • Zelang Miao

Abstract

Standard deviational ellipse (SDE) has long served as a versatile GIS tool for delineating the geographic distribution of concerned features. This paper firstly summarizes two existing models of calculating SDE, and then proposes a novel approach to constructing the same SDE based on spectral decomposition of the sample covariance, by which the SDE concept is naturally generalized into higher dimensional Euclidean space, named standard deviational hyper-ellipsoid (SDHE). Then, rigorous recursion formulas are derived for calculating the confidence levels of scaled SDHE with arbitrary magnification ratios in any dimensional space. Besides, an inexact-newton method based iterative algorithm is also proposed for solving the corresponding magnification ratio of a scaled SDHE when the confidence probability and space dimensionality are pre-specified. These results provide an efficient manner to supersede the traditional table lookup of tabulated chi-square distribution. Finally, synthetic data is employed to generate the 1-3 multiple SDEs and SDHEs. And exploratory analysis by means of SDEs and SDHEs are also conducted for measuring the spread concentrations of Hong Kong’s H1N1 in 2009.

Suggested Citation

  • Bin Wang & Wenzhong Shi & Zelang Miao, 2015. "Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-17, March.
    • Handle: RePEc:plo:pone00:0118537
    DOI: 10.1371/journal.pone.0118537
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118537
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0118537&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0118537?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
    ---><---

    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:plo:pone00:0118537. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.