Exact Distributions for χ2 and for the Likelihood-Ratio Statistic for the Equiprobable Multinomial Distribution

Abstract A sample of size N is taken from an equiprobable t-category multinomial distribution. The precise values of Pearson's X 2 and the likelihood ratio statistic A were computed for t = 3(1)6, N = 3(1)12; t = 6(1)14, N = 6(1)2t; t=15(1)18, N = 6(1)28. The logarithms of the tail areas were smoothed and fitted by means of quadratic expressions. Much information is given concerning the accuracy of the chi-squared fits to the distributions of X 2 and A. A table of −log10 P(χ2 > a) is given, for a = 1(1)50, and d.f. = 1(1)20. The distribution of the total number of repeats within cells is also discussed.

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