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检验方差之间线性关系的若干程序AI 解读

Summary In this paper, procedures are given for testing the hypothesis that the relation σ32=σ12+σ22 holds among the three variances σ12,σ22 and α32. This hypothesis is tested against the alternatives (i) σ32>σ12+σ22, (ii) σ32<σ12+σ22 and (iii) σ32≠σ12+σ22. The test procedures satisfy the property that the size or the Type I error does not exceed the preassigned level α. Optimum properties of the tests and their size and power functions are also investigated. The…

等概率检验及其在若干同时推断问题中的应用AI 解读

Consider the problem of testing the hypothesis H 0: θ ∈ W 0 against the alternative H 1: θ ∈ W 1 when a certain subset E 0 ⊂ W 1 is given. This subset E 0 is such that the risk of accepting H 0 will be significant economically only if θ ∈ E 0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations…

等概率检验及其在若干同时推断问题中的应用AI 解读

Consider the problem of testing the hypothesis H 0: θ ∈ W 0 against the alternative H 1: θ ∈ W 1 when a certain subset E 0 ⊂ W 1 is given. This subset E 0 is such that the risk of accepting H 0 will be significant economically only if θ ∈ E 0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations…