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幂散度拟合优度统计量的小样本比较AI 解读

The small-sample properties of the power divergence family of goodness-of-fit statistics (Cressie and Read in press) are examined. The asymptotic χ2 and three alternative approximations are used to obtain appropriate test levels for comparison with the exact level. It is shown that if the χ2 approximation is to be used, then there are many preferable statistics to the log-likelihood ratio G 2 (including Pearson's χ2). Furthermore, exact power comparisons under specific…

多项分布的拟合优度检验AI 解读

SUMMARY This article investigates the family {I λ;λ ϵ ℝ} of power divergence statistics for testing the fit of observed frequencies {Xi; i = 1, …, k} to expected frequencies {Ei; i = 1, …, k}. From the definition 2nIλ=2λ(λ+1)∑i=1kXi{(XiEi)λ−1};λ∈ℝ it can easily be seen that Pearson's X 2 (λ = 1), the log likelihood ratio statistic (λ = 0), the Freeman-Tukey statistic (λ = –½) the modified log likelihood ratio statistic (λ = –1) and the Neyman modified X 2 (λ = –2), are all…