A Bootstrap Test for Symmetry based on Cumulative Entropy

Document Type : Original Paper

Author

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

Abstract

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.

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References

[1] Wang, M.L.(1996). Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A., 213, 279-287.
 
[2] Yang, L., Liu, J.B. and Yang, K.Q. (2001).Exact solutions of nonlinear PDE, nonlinear transformations and reduction of nonlinear PDE to a quadrature, Phys. Lett. A., 278, 267-270.
 
[3] Fan, E.G. (2000). Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A., 277, 212-218.
[4] Ismail, H.N.A., Raslan, K. and Rabboh, A.A.A. (2004). Adomian decomposition method for Burger’s-Huxley and Burger’s-Fisher equations, Appl. Math. Comput., 159, 291-301.
 
[5] Hashim, I., Noorani, M.S.M. and Batiha, B. (2006). A note on the Adomian decomposition method for the generalized Huxley equation, Appl. Math. Comput., 181, 1439-1445.
 
[6] Yan, Z.Y. and Zhang, H.Q. (1999). New explicit and exact travelling wave solutions for a system of variant boussinesq equations in mathematical physics, Phys. Lett. A., 252, 291-296.
Journal of Advanced Mathematical Modeling
Volume 6, Issue 2
December 2016
Pages 1-14

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History

  • Receive Date: 05 December 2015
  • Revise Date: 14 June 2017
  • Accept Date: 20 September 2016

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