The Likelihood Ratio Test for Poisson Versus Binomial Distributions
研究了在二项分布中估计N的难题，将其视为边界值检验问题，证明了检验N为无穷（即数据服从泊松分布）的偏差统计量的渐近分布是点质量零和卡方分布的50-50混合，并讨论了小样本下该近似的不足及方法应用。
Abstract The estimation of N in the binomial B(N, p) distribution is a considerably harder problem than the estimation of p. We approach it as a “boundary value” estimation and testing problem, where the boundary N = ∞ corresponds to a Poisson distribution for the data, whereas N < ∞ corresponds to a binomial distribution. The asymptotic distribution of the deviance statistic for testing the hypothesis that the true value of N is infinite is shown to be a 50–50 mixture between a point mass at zero and a chi-squared distribution. We show also that the asymptotic distribution is not a good approximation for small samples, discuss the application of the method, and compare it to alternative approaches.