On homogeneous skewness of unimodal distributions

Shubhabrata Das, Pranab K. Mandal, Diptesh Ghosh

    Research output: Book/ReportReportProfessional

    306 Downloads (Pure)


    We introduce a new concept of skewness for unimodal continuous distributions which is built on the asymmetry of the density function around its mode. The asymmetry is captured through a skewness function. We call a distribution homogeneously skewed if this skewness function is consistently positive or negative throughout its domain, and partially homogeneously skewed if the skewness function changes its sign at most once. This type of skewness is shown to exist in many popular continuous distributions such as Triangular, Gamma, Beta, Lognormal and Weibull. Two alternative ways of partial ordering among the partially homogeneously skewed distributions are described. Extensions of the notion to broader classes of distributions including discrete distributions have also been discussed.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages18
    Publication statusPublished - Dec 2009

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850


    • EWI-16931
    • IR-68741
    • METIS-264198
    • Skewness function
    • Probability distribution
    • MSC-60E05
    • Statistics

    Cite this