Approximating the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit
研究了多项分布拟合优度检验中似然比统计量G²的均值和方差的近似公式，精度达到O(N⁻³)，并发现当类别数k≥4时渐近卡方分布拟合不佳，而乘性校正和贝塔分布方法可改善拟合效果。
Abstract Approximations were derived for the mean and variance of G 2, the likelihood ratio statistic for testing goodness of fit in a k cell multinomial distribution. These approximate moments, accurate to O(N -3), may be used in fitting the distribution of G 2. Extensive numerical studies of the exact and approximate distributions were performed in the special case of equiprobability. The asymptotic chi-squared distribution was found to fit poorly for k ≥ 4. Satisfactory results were obtained using a multiplicative correction to the chi-squared fit. More sophisticated procedures using the beta distribution produced increased accuracy, but at the cost of excessive computational labor.