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Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

机译：通过其特征函数的数值反演计算Bartlett测试统计的确切分布

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摘要

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes.
机译：应用精确的统计推理经常导致所考虑的估计或测试统计的非标准概率分布。许多估算器和测试统计数据的确切分布可以通过其特征函数指定，因此Bartlett的测试统计数据的空分布是一种情况。然而，如果可能的话，特征函数的分析反演通常会导致用于计算分发函数和相应的量级的复杂表达式。有效的替代方案是基于特征函数的数值反演的众所周知的方法，然而，在流行的统计软件包中忽略了这一点。在本文中，我们介绍了校正的Bartlett的测试统计的明确特征函数以及基于该特征函数的数值反演的方法的计算快速高效地实现，建议评估用于测试差异的均匀性的精确空分布几个正常种群，采用可能不等的样本尺寸。

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