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An empirical likelihood ratio based goodness-of-fit test for skew normality

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  • Wei Ning
  • Grace Ngunkeng

Abstract

In this paper, an empirical likelihood ratio based goodness-of-fit test for the skew normality is proposed. The asymptotic results of the test statistic under the null hypothesis and the alternative hypothesis are derived. Simulations indicate that the Type I error of the proposed test can be well controlled for a given nominal level. The power comparison with other available tests shows that the proposed test is competitive. The test is applied to IQ scores data set and Australian Institute of Sport data set to illustrate the testing procedure. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Wei Ning & Grace Ngunkeng, 2013. "An empirical likelihood ratio based goodness-of-fit test for skew normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 209-226, June.
    • Handle: RePEc:spr:stmapp:v:22:y:2013:i:2:p:209-226
    DOI: 10.1007/s10260-012-0218-z
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    References listed on IDEAS

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    1. C. C. Figueiredo & H. Bolfarine & M. C. Sandoval & C. R. O. P. Lima, 2010. "On the skew-normal calibration model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 435-451.
    2. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    3. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
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    Cited by:

    1. Wenhao Gui & Lei Guo, 2018. "Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(4), pages 633-650, December.
    2. Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2015. "A new powerful version of the BUS test of normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 449-474, September.

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