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文章基本信息

  • 标题:On combining the zero bias transform and the empirical characteristic function to test normality
  • 本地全文:下载
  • 作者:Bruno Ebner
  • 期刊名称:Latin American Journal of Probability and Mathematical Statistics
  • 电子版ISSN:1980-0436
  • 出版年度:2021
  • 卷号:18
  • 期号:1
  • 页码:1029
  • DOI:10.30757/ALEA.v18-38
  • 出版社:Instituto Nacional De Matemática Pura E Aplicada
  • 摘要:We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero bias transform. Limit distributions of the test statistics are provided under the null hypothesis, as well as under contiguous and fixed alternatives. Using the covariance structure of the limiting Gaussian process from the null distribution, we derive explicit formulas for the first four cumulants of the limiting random element and apply the results by fitting a distribution from the Pearson system. A comparative Monte Carlo power study shows that the new tests are serious competitors to the strongest well established tests.
  • 其他关键词:Goodness-of-fit, Normal Distribution, Stein’s Method, Zero Bias Transformation, Empirical Characteristic Function.
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