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MODELLING ZERO-INFLATED COUNT DATA WITH A SPECIAL CASE OF THE GENERALISED POISSON DISTRIBUTION

Published online by Cambridge University Press:  04 September 2019

Enrique Calderín-Ojeda ,
Emilio GóMez-Déniz  and
Inmaculada Barranco-Chamorro
Enrique Calderín-Ojeda
Affiliation:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Victoria 3010, Australia E-Mail: enrique.calderin@unimelb.edu.au
Emilio GóMez-Déniz
Affiliation:
Department of Quantitative Methods and Institute of Tourism and, Sustainable Economic Development (TIDES), University of Las Palmas de Gran Canaria, 35017 Las Palmas, Spain, E-Mail: emilio.gomez-deniz@ulpgc.es
Inmaculada Barranco-Chamorro
Affiliation:
Facultad de Matemáticas. Department of Matematics and RO, University of Sevilla, 41012 Sevilla, Spain, E-Mail: chamorro@us.es
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Abstract

A one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is unimodal with a zero vertex and over-dispersed. A generalised linear model related to this distribution is also presented. Its parameters can be estimated by using a Fisher-Scoring algorithm which is equivalent to iteratively reweighted least squares. Due to its flexibility and capacity to describe highly skewed data with an excessive number of zeros, the model is suitable to be applied in insurance settings as an alternative to the negative binomial and zero-inflated model.

Keywords

Zero-inflated count datageneralised linear modelsgeneralised Poisson distributionautomobile insurancefisher-scoring algorithmrandomised quantile residuals60E0562E9960J80
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 689 - 707
Copyright
© Astin Bulletin 2019 

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