MODELLING ZERO-INFLATED COUNT DATA WITH A SPECIAL CASE OF THE GENERALISED POISSON DISTRIBUTION
Enrique Calderin-Ojeda, Emilio Gomez-Deniz, Inmaculada Barranco-Chamorro
ASTIN Bulletin | Cambridge University Press (CUP) | Published : 2019
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.
Awarded by Ministerio de Economia y Competitividad, Spain
Awarded by Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion, Spain
The authors greatly appreciate the comments made by the Editor as well as by two anonymous reviewers who have contributed to substantially improve this work. Research partially carried out while Calderin-Ojeda visited IMUS (University of Sevilla) as part of his Special Study Program leave. This work was partially funded by grants ECO2013-47092 (Ministerio de Economia y Competitividad, Spain) and ECO2017-85577-P (Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion, Spain).