IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v27y2000i4p657-671.html
   My bibliography  Save this article

A Third Order Point Process Characteristic

Author

Listed:
  • K. Schladitz
  • A. J. Baddeley

Abstract

Second order characteristics, in particular Ripley's K‐function, are widely used for the statistical analysis of point patterns. We examine a third order analogue, namely the mean number T(r) of r‐close triples of points per unit area. Equivalently this is the expected number of r‐close point pairs in an r‐neighbourhood of the typical point. Various estimators for this function are proposed and compared, and we give an explicit formula for the isotropic edge correction. The theoretical value of T seems to be unobtainable for most point process models apart from the homogeneous Poisson process. However, simulation studies show that the function T discriminates well between different types of point processes. In particular it detects a clear difference between the Poisson process and the Baddeley–Silverman cell process whereas the K‐functions for these processes coincide.

Suggested Citation

  • K. Schladitz & A. J. Baddeley, 2000. "A Third Order Point Process Characteristic," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 657-671, December.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:4:p:657-671
    DOI: 10.1111/1467-9469.00214
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9469.00214
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9469.00214?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
    ---><---

    Citations

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


    Cited by:

    1. Wu, Liu-Cang & Li, Hui-Qiong, 2009. "Summary statistics for measuring the relationship among three types of points in multivariate point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2809-2816, June.
    2. Tscheschel, A. & Stoyan, D., 2006. "Statistical reconstruction of random point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 859-871, November.
    3. Jalilian, Abdollah, 2016. "On the higher order product density functions of a Neyman–Scott cluster point process," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 144-150.
    4. Carlos Comas & Jorge Mateu & Aila Särkkä, 2010. "A third‐order point process characteristic for multi‐type point processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 19-44, February.

    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:bla:scjsta:v:27:y:2000:i:4:p:657-671. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.