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

Paul J. Smith, Donald S. Rae, Ronald W. Manderscheid and Sam Silbergeld
Journal of the American Statistical Association
Vol. 76, No. 375 (Sep., 1981), pp. 737-740
DOI: 10.2307/2287541
Stable URL: http://www.jstor.org/stable/2287541
Page Count: 4
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Approximating the Moments and Distribution of the Likelihood Ratio Statistic for Multinomial Goodness of Fit
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Abstract

Approximations were derived for the mean and variance of G2, 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 G2. 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.

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