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样本相关系数分布的若干新结果AI 解读

Summary A simple approximate normalization for the correlation coefficient in normal samples is obtained which is shown to compare favourably with previous normalization approximations (the usual large-sample normalization, Fisher's hyperbolic tangent transformation and Hotelling's improvement of that transformation). A second approximation, based on F and valid for large n | ρ | (n = sample size, ρ = population correlation), is also obtained. The results follow from a…

正态概率积分与 Mills 比率的新渐近展开AI 解读

SUMMARY Mill’s ratio can be expressed, for positive values of the argument x, as the Laplace transform, with argument x, of the function e−12t2. This enables a new, and superior, asymptotic expansion for Mill’s ratio to be obtained with the aid of a recent result on the asymptotic expansions of a wide class of Laplace transforms. The new expansion is considerably more accurate than the usual expansion.