Departamento de Estadística e IO, Universidad de Sevilla, Sevilla, Spain.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain.
Biom J. 2020 Jul;62(4):970-988. doi: 10.1002/bimj.201900185. Epub 2020 Jan 29.
A recent method for estimating a lower bound of the population size in capture-recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent for count distributions having a log-convex pgf ( -class). This is a large family that includes mixed and compound Poisson distributions, and their independent sums and finite mixtures as well. The finite-sample performance of the lower bound estimator is assessed via simulation showing a better behavior than some close competitors. Several examples of application are also analyzed and discussed.
本文研究了一种最近提出的用于估计捕获-再捕获样本中种群大小下界的方法。具体来说，提供了一些渐近性质，如强一致性和渐近正态性。所提出的估计量基于观测数据的经验概率生成函数（pgf），并且对于具有对数凸 pgf（ - 类）的计数分布是一致的。这是一个包括混合泊松分布和复合泊松分布、它们的独立和以及有限混合的大的家族。通过模拟评估了下界估计量的有限样本性能，结果表明它比一些相近的竞争者表现更好。还分析和讨论了几个应用实例。
