Inference for the Parameters of a Zero-Inflated Poisson Predictive Model

In the insurance sector, Zero-Inflated models are commonly used due to the unique nature of insurance data, which often contain both genuine zeros (meaning no claims made) and potential claims. Although active developments in modeling excess zero data have occurred, the use of Bayesian techniques fo...

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Bibliographic Details
Published in:Risks (Basel) 2024-07, Vol.12 (7), p.104
Main Authors: Deng, Min, Aminzadeh, Mostafa S., So, Banghee
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Bayesian analysis
bayesian estimation
beta distribution
Binomial distribution
Expected values
Flexibility
gamma distribution
Insurance claims
ML estimation
Monte Carlo simulation
Parameter estimation
Random variables
score test
zero-inflated poisson model
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Summary:In the insurance sector, Zero-Inflated models are commonly used due to the unique nature of insurance data, which often contain both genuine zeros (meaning no claims made) and potential claims. Although active developments in modeling excess zero data have occurred, the use of Bayesian techniques for parameter estimation in Zero-Inflated Poisson models has not been widely explored. This research aims to introduce a new Bayesian approach for estimating the parameters of the Zero-Inflated Poisson model. The method involves employing Gamma and Beta prior distributions to derive closed formulas for Bayes estimators and predictive density. Additionally, we propose a data-driven approach for selecting hyper-parameter values that produce highly accurate Bayes estimates. Simulation studies confirm that, for small and moderate sample sizes, the Bayesian method outperforms the maximum likelihood (ML) method in terms of accuracy. To illustrate the ML and Bayesian methods proposed in the article, a real dataset is analyzed.
ISSN:2227-9091
2227-9091
DOI:10.3390/risks12070104