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Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution

Author

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  • Wenhao Gui

    (Beijing Jiaotong University)

  • Lei Guo

    (Beijing Jiaotong University)

Abstract

In this paper, we consider the problem of estimating the location and scale parameters of the skew normal distribution introduced by Azzalini. For this distribution, the classic maximum likelihood estimators(MLEs) do not take explicit forms. We approximate the likelihood equations and derive explicit estimators of the parameters. The bias and variance of the estimators are investigated and Monte Carlo simulation studies show that the estimators are as efficient as the classic MLEs. We demonstrate that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory, especially when the sample size is small. The use of unconditional simulated percentage points of these quantities is suggested. Finally, a numerical example is used to illustrate the proposed inference methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:4:d:10.1007_s13226-018-0291-6
    DOI: 10.1007/s13226-018-0291-6
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    References listed on IDEAS

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    1. 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.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. 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.
    4. Ahmed Hossain & Joseph Beyene, 2015. "Application of skew-normal distribution for detecting differential expression to microRNA data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 477-491, March.
    5. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    6. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 1-13, April.
    7. A. Asgharzadeh & L. Esmaily & S. Nadarajah, 2013. "Approximate MLEs for the location and scale parameters of the skew logistic distribution," Statistical Papers, Springer, vol. 54(2), pages 391-411, May.
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