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The empirical characteristic function is found to be effectively applied to test for the shape of distribution. The squared modulus of the studentized empirical characteristic function is suggested for testing the composite hypothesis that μ + σX is subject to a known distribution, for unknown constants μ and σ. It is shown that the studentized empirical characteristic function, if properly normalized, converges weakly to a complex Gaussian process. Asymptotic…

学生化经验特征函数及其分布形状检验应用AI 解读

The empirical characteristic function is found to be effectively applied to test for the shape of distribution. The squared modulus of the studentized empirical characteristic function is suggested for testing the composite hypothesis that μ + σX is subject to a known distribution, for unknown constants μ and σ. It is shown that the studentized empirical characteristic function, if properly normalized, converges weakly to a complex Gaussian process. Asymptotic…