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A nonparametric method of estimation of the population size in capture–recapture experiments
Author(s) -
JiménezGamero María Dolores,
Puig Pedro
Publication year - 2020
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201900185
Subject(s) - mathematics , estimator , asymptotic distribution , nonparametric statistics , consistency (knowledge bases) , statistics , sample size determination , poisson sampling , poisson distribution , mark and recapture , population , importance sampling , monte carlo method , discrete mathematics , demography , sociology , slice sampling
Abstract 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 ( L C ‐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.