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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

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
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
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%.
1932-6157
1198-1211
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Van Der Heijden, Peter
85157917-3b33-4683-81be-713f987fd612
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Van Der Heijden, Peter
85157917-3b33-4683-81be-713f987fd612

Bohning, Dankmar and Van Der Heijden, Peter (2019) 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. The Annals of Applied Statistics, 13 (2), 1198-1211. (doi:10.1214/18-AOAS1232).

Record type: Article

Abstract

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%.

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Accepted/In Press date: 30 November 2018
e-pub ahead of print date: 17 June 2019
Published date: 2019

Identifiers

Local EPrints ID: 426678
URI: http://eprints.soton.ac.uk/id/eprint/426678
ISSN: 1932-6157
PURE UUID: 41113446-1fcc-4094-8b0e-87916ac79a1d
ORCID for Dankmar Bohning: ORCID iD orcid.org/0000-0003-0638-7106
ORCID for Peter Van Der Heijden: ORCID iD orcid.org/0000-0002-3345-096X

Catalogue record

Date deposited: 10 Dec 2018 17:31
Last modified: 18 Feb 2021 17:21

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