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样本量不超过 25 时 b1 的零分布及数值表AI 解读

For the sampling distribution of √b1 in samples of size n from a normal parent, leading singular terms of the density fn at its singularities are obtained by application of a general method given previously. These terms are combined with correcting terms, fitted by moments, to give approximations to fn, integrals of which were used to compute a table of the distribution function Fn for 4 ≤ n ≤ 12: for l3 ≤ n ≤ 25 Gram-Charlier expansions were used. A recurrence for the…

抽样分布的奇异性：尤其是二次型之比AI 解读

A general theory of singularities in sampling distributions, given previously for statistical functions on a Euclidean space, is here extended to functions on a hypersphere; in particular, to distributions of ratios of quadratic forms. The parent distributions chiefly considered are normal and nonsingular. The theory expresses the density of a sampling distribution as the sum of a singular function and a smoother remainder. Cases are adduced in which the remainder vanishes:…

抽样分布的奇异性：特别是二次型比值的分布AI 解读

A general theory of singularities in sampling distributions, given previously for statistical functions on a Euclidean space, is here extended to functions on a hypersphere; in particular, to distributions of ratios of quadratic forms. The parent distributions chiefly considered are normal and nonsingular. The theory expresses the density of a sampling distribution as the sum of a singular function and a smoother remainder. Cases are adduced in which the remainder vanishes:…