A Bootstrap Test for Symmetry based on Cumulative Entropy

Document Type : Original Paper


Department of Statistics, University of Mohaghegh Ardabili, Ardabil, Iran


The symmetry assumption plays an important role in nonparametric statistical inference methods. Using different measure of asymmetry, various test statistics has proposed for testing the symmetry hypothesis. In this paper, we apply the cumulative residual entropy to introduce a new skewness measure and construct a distribution–free test for the hypothesis. Bootstrap re-sampling from a symmetric empirical distribution function is used to calculate the p-value of the test. The power of the new test statistic is compared with two existing tests in a simulation study. The results show that the proposed test preserves its level and it has reasonable power properties on the family of distribution evaluated.


Main Subjects

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Volume 6, Issue 2
December 2016
Pages 1-14
  • Receive Date: 05 December 2015
  • Revise Date: 14 June 2017
  • Accept Date: 20 September 2016
  • First Publish Date: 19 February 2017