Measuring asymmetry and testing symmetry

Christopher Partlett, Prakash Patil

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)
    953 Downloads (Pure)

    Abstract

    In this paper, we show that some of the most commonly used tests of symmetry do not have power which is reflective of the size of asymmetry. This is because the primary rationale for the test statistics that are proposed in the literature to test for symmetry is to detect the departure from symmetry, rather than the quantification of the asymmetry. As a result, tests of symmetry based upon these statistics do not necessarily generate power that is representative of the departure from the null hypothesis of symmetry. Recent research has produced new measures of asymmetry, which have been shown to do an admirable job of quantifying the amount of asymmetry. We propose several new tests based upon one such measure. We derive the asymptotic distribution of the test statistics and analyse the performance of these proposed tests through the use of a simulation study.
    Original languageEnglish
    Pages (from-to)1-32
    JournalInstitute of Statistical Mathematics. Annals
    Early online date14 Dec 2015
    DOIs
    Publication statusE-pub ahead of print - 14 Dec 2015

    Keywords

    • symmetry
    • asymmetry
    • measure of asymmetry
    • testing symmetry
    • skewness

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