A Numerical Study of the Power Function of a New Symmetry Test

  • D. BagkavosEmail author
  • P. N. Patil
  • A. T. A. Wood
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 175)


A new nonparametric test for the null hypothesis of symmetry is proposed. A necessary and sufficient condition for symmetry, which is based on the fact that under symmetry the covariance between the probability density and cumulative distribution functions of the underlying population is zero, is used to define the test statistic. The main emphasis here is on the small sample power properties of the test. Through simulations with samples generated from a wide range of distributions, it is shown that the test has a reasonable power function which compares favorably against many other existing tests of symmetry. It is also shown that the defining feature of this test is “the higher the asymmetry higher is the power”.


Asymmetry Skewness Nonparametric estimation Correlation 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.AccentureAthensGreece
  2. 2.Department of Mathematics and StatisticsMississippi State UniversityMississippiUSA
  3. 3.School of Mathematical SciencesThe University of NottinghamNottinghamUK

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