Approximating the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit.

Approximations were derived for the mean and variance of G[sup 2], the likelihood ratio statistic for testing goodness of fit in a k cell multinomial distribution. These approximate moments, accurate to O(N[sup -3]), may be used in fitting the distribution of G[sup 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. [ABSTRACT FROM AUTHOR]