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Calderín-Ojeda, Enrique; Gómez-Déniz, Emilio; Barranco-Chamorro, Inmaculada

Modelling zero-inflated count data with a special case of the generalised Poisson distribution. (English) Zbl 1427.91220

ASTIN Bull. 49, No. 3, 689-707 (2019).
Summary: A one-parameter version of the generalised Poisson distribution provided by P. C. Consul and G. C. Jain [Technometrics 15, 791–799 (1973; Zbl 0271.60020)] 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.

Cited in 3 Documents

MSC:

91G05 Actuarial mathematics
62P05 Applications of statistics to actuarial sciences and financial mathematics

Keywords:

zero-inflated count data; generalised linear models; generalised Poisson distribution; automobile insurance; Fisher-scoring algorithm; randomised quantile residuals

Citations:

Zbl 0271.60020
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Full Text: DOI

References:

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