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We consider a multinomial distribution, where the number of cells increasesand the cell-probabilities decreases as the number of observations grows. Theprobabilities of large deviations of statistics, which has form of a sum ofBorel functions of cell-frequencies, are studied. Large deviation results forthe power-divergence statistics and its most popular special variants, as wellas for some count statistics are derived as consequences of general theorems.

The Probabilities of Large Deviations Associated with Multinomial Distributions