Non‐parametric Estimation of the Number of Zeros in Truncated Count Distributions
针对具有对数凸概率生成函数的计数分布，给出了零概率的下界，并据此构建了未观测零个数的非参数估计量，适用于捕获再捕获模型、流行病学和文学风格分析等领域。
Abstract We present some lower bounds for the probability of zero for the class of count distributions having a log‐convex probability generating function, which includes compound and mixed‐Poisson distributions. These lower bounds allow the construction of new non‐parametric estimators of the number of unobserved zeros, which are useful for capture‐recapture models, or in areas like epidemiology and literary style analysis. Some of these bounds also lead to the well‐known Chao's and Turing's estimators. Several examples of application are analysed and discussed.