Multinomial probabilities and the ϰ 2 and X 2 distributions
多项分布概率与卡方分布
The usual approximation to the logarithm of a multinomial probability correctly gives its asymptotic limit in terms of the X2 distribution (of sums of squares of normal deviates) and the X2 statistic (sum of [observed minus expected]2/expected frequency), but not how it approaches this limit. A formula is derived that appears to be valid under wider conditions; this also throws light on the range of validity of the X2 goodness-of-fit test, and the relation of the log of the…