Böhning, Dankmar; van der Heijden, Peter G. M. The identity of the zero-truncated, one-inflated likelihood and the zero-one-truncated likelihood for general count densities with an application to drink-driving in Britain. (English) Zbl 1423.62134 Ann. Appl. Stat. 13, No. 2, 1198-1211 (2019). Summary: For zero-truncated count data, as they typically arise in capture-recapture modelling, we consider modelling under one-inflation. This is motivated by police data on drink-driving in Britain which shows high one-inflation. The data, which are used here, are from the years 2011 to 2015 and are based on DR10 endorsements. We show that inference for an arbitrary count density with one-inflation can be equivalently based upon the associated zero-one truncated count density. This simplifies inference considerably including maximum likelihood estimation and likelihood ratio testing. For the drink-driving application, we use the geometric distribution which shows a good fit. We estimate the total drink-driving as about \(2,300,000\) drink-drivers in the observational period. As \(227,578\) were observed, this means that only about 10% of the drink-driving population is observed with a bootstrap confidence interval of 9%–12%. Cited in 9 Documents MSC: 62P10 Applications of statistics to biology and medical sciences; meta analysis 62G07 Density estimation 62H12 Estimation in multivariate analysis 62G15 Nonparametric tolerance and confidence regions 62G09 Nonparametric statistical resampling methods 62P15 Applications of statistics to psychology Keywords:capture-recapture; Chao estimator; behavioral response; power series distribution; mixture model; zero-truncated model; nonparametric estimator of population size Software:bootstrap × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Anan, O., Böhning, D. and Maruotti, A. (2017). Uncertainty estimation in heterogeneous capture-recapture count data. J. Stat. Comput. 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