Accurate Normalizing Transformations of a Student's t Variate
提出了两种将学生t变量转换为正态分布的变换，一种在整体上比已有变换更精确，另一种在标准正态分布的指定分位点处局部精确，可用于构建检验统计量或简化软件中的t检验。
SUMMARY Two normalizing transformations of a Student's t variate are proposed. One is more accurate uniformly than any transformation previously given, while the other is very accurate locally at a prescribed deviate of the standard normal distribution. A NUMBER of authors have suggested transformations that normalize a Student's t variate; some of these are compared in Prescott (1974). Such transformations have several applications: they can be used in the construction of a single test statistic from a number of calculated t values; and they can be included in computer software packages so that, for instance, a t test can be carried out with the need for only a few critical values of the normal distribution to be stored. In view of this latter point, there is a particular need for a transformation that is accurate locally at a prescribed deviate of the standard normal distribution. In this paper we derive such a transformation along with another that is more accurate uniformly than any previously given. Both transformations, like their precursors, can be evaluated easily on a modest electronic calculator.