A New F Approximation for the Pillai-Bartlett Trace under H 0
针对Pillai-Bartlett迹统计量在零假设下的近似，提出了两种新的F分布近似方法，在保持逻辑性质的同时，数值精度接近Pillai的第二种近似，优于广泛使用的第一种近似。
Pillai suggested two approximations for the Pillai–Bartlett trace statistic in the null case. The first one matches one moment of a β1 random variable, and corresponds to an F random variable, and the second matches four moments in the Pearson system. Although intuitively appealing and widely used in current statistical packages, the first lacks accuracy even with moderate sample size. The second matches two moment ratios in the Pearson system and provides much greater accuracy. Two new approximations match two moments of a β1 random variable, and hence correspond to an F random variable, yet achieve most of the accuracy of Pillai’s second approximation. The second of the two new approximations provides the best combination of logical properties and numerical accuracy.