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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China

    Wenhao Gui & Lei Guo

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  1. Wenhao Gui
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  2. Lei Guo
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Correspondence to Wenhao Gui.

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Gui, W., Guo, L. Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution. Indian J Pure Appl Math 49, 633–650 (2018). https://doi.org/10.1007/s13226-018-0291-6

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  • DOI: https://doi.org/10.1007/s13226-018-0291-6

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