Journal
ASTIN BULLETIN
Volume 49, Issue 3, Pages 689-707Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/asb.2019.26
Keywords
Zero-inflated count data; generalised linear models; generalised Poisson distribution; automobile insurance; fisher-scoring algorithm; randomised quantile residuals
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Funding
- Ministerio de Economia y Competitividad, Spain [ECO2013-47092]
- Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion, Spain [ECO2017-85577-P]
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A one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is uni- modal 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.
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