IDEAS home Printed from
   My bibliography  Save this article

Estimating Allele Frequencies and Inbreeding Coefficients in K-Allele Models


  • Prakash Gorroochurn
  • Susan Hodge


Some of the methods of estimation of allele frequencies and inbreeding coefficients in a K-allele model are examined. A result that has long been assumed to be true is proved. That is, in the presence of inbreeding, the maximum likelihood estimators of the allele frequencies and of the inbreeding coefficient f do not in general equal their observed (or sample) values (except when K = 2). A least-squares way of looking at the estimation problem is presented, and simulations are used to compare the three types of estimators (sample, maximum likelihood, and least-squares) in a 3-allele model. Probability generating functions are used to derive exact expressions for the bias of the sample estimator of f in a 2-allele model for any sample size, and those biases are calculated for a number of situations. Finally, an approximately unbiased estimator of the inbreeding coefficient when an allele is rare or common is proposed, and its bias is compared with that of the sample estimator and with that of an estimator proposed by Weir (1996).

Suggested Citation

  • Prakash Gorroochurn & Susan Hodge, 2006. "Estimating Allele Frequencies and Inbreeding Coefficients in K-Allele Models," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(2), pages 83-103.
  • Handle: RePEc:taf:mpopst:v:13:y:2006:i:2:p:83-103
    DOI: 10.1080/08898480600620027

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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


    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:taf:mpopst:v:13:y:2006:i:2:p:83-103. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.