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

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Nonparametric Statistics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 175))

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Abstract

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”.

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Author information

Authors and Affiliations

  1. Accenture, Rostoviou 39–41, 11526, Athens, Greece

    D. Bagkavos

  2. Department of Mathematics and Statistics, Mississippi State University, Mississippi, USA

    P. N. Patil

  3. School of Mathematical Sciences, The University of Nottingham, Nottingham, UK

    A. T. A. Wood

Authors
  1. D. Bagkavos
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  2. P. N. Patil
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  3. A. T. A. Wood
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Corresponding author

Correspondence to D. Bagkavos .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Universidade da Coruña, A Coruña, Spain

    Ricardo Cao

  2. Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain

    Wenceslao González Manteiga

  3. Department of Statistics, Universidad Carlos III de Madrid, Getafe, Spain

    Juan Romo

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Bagkavos, D., Patil, P.N., Wood, A.T.A. (2016). A Numerical Study of the Power Function of a New Symmetry Test. In: Cao, R., González Manteiga, W., Romo, J. (eds) Nonparametric Statistics. Springer Proceedings in Mathematics & Statistics, vol 175. Springer, Cham. https://doi.org/10.1007/978-3-319-41582-6_1

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