Boston University Libraries OpenBU
    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    •   OpenBU
    • BU Open Access Articles
    • BU Open Access Articles
    • View Item
    •   OpenBU
    • BU Open Access Articles
    • BU Open Access Articles
    • View Item

    Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions

    Thumbnail
    Date Issued
    2019-02-01
    Publisher Version
    10.1016/j.physa.2018.09.049
    Author(s)
    Nelson, Kenric P.
    Kon, Mark A.
    Umarov, Sabir R.
    Share to FacebookShare to TwitterShare by Email
    Export Citation
    Download to BibTex
    Download to EndNote/RefMan (RIS)
    Metadata
    Show full item record
    Permanent Link
    https://hdl.handle.net/2144/38449
    Version
    Accepted manuscript
    Citation (published version)
    Kenric P Nelson, Mark A Kon, Sabir R Umarov. 2019. "Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions." PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, Volume 515, pp. 248 - 257. https://doi.org/10.1016/j.physa.2018.09.049
    Abstract
    The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student’s t distribution. The coupled Gaussian is a member of a family of distributions parameterized by the nonlinear statistical coupling which is the reciprocal of the degree of freedom and is proportional to fluctuations in the inverse scale of the Gaussian. Existing estimators of the scale of the coupled Gaussian have relied on estimates of the full distribution, and they suffer from problems related to outliers in heavy-tailed distributions. In this paper, the scale of a coupled Gaussian is proven to be equal to the product of the generalized mean and the square root of the coupling. From our numerical computations of the scales of coupled Gaussians using the generalized mean of random samples, it is indicated that only samples from a Cauchy distribution (with coupling parameter one) form an unbiased estimate with diminishing variance for large samples. Nevertheless, we also prove that the scale is a function of the geometric mean, the coupling term and a harmonic number. Numerical experiments show that this estimator is unbiased with diminishing variance for large samples for a broad range of coupling values.
    Collections
    • CAS: Mathematics & Statistics: Scholarly Works [332]
    • BU Open Access Articles [4751]


    Boston University
    Contact Us | Send Feedback | Help
     

     

    Browse

    All of OpenBUCommunities & CollectionsIssue DateAuthorsTitlesSubjectsThis CollectionIssue DateAuthorsTitlesSubjects

    Deposit Materials

    LoginNon-BU Registration

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Boston University
    Contact Us | Send Feedback | Help