The Studentized Empirical Characteristic Function and Its Application to Test for the Shape of Distribution
提出基于学生化经验特征函数的统计量，用于检验数据是否服从已知分布（如正态性），模拟显示该检验在某些备择假设下比峰度检验更有效。
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 considerations, as well as computer simulation, reveal that the proposed statistic, when applied to test normality, is more efficient than, or as efficient as, the test by the sample kurtosis, for certain types of alternatives.