零膨胀泊松预测模型参数推理

IF 2 Q2 BUSINESS, FINANCE Risks Pub Date : 2024-06-24 DOI:10.3390/risks12070104
Min Deng, Mostafa S. Aminzadeh, Banghee So
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引用次数: 0

摘要

在保险领域,由于保险数据的特殊性,通常既包含真正的零(即无赔付),也包含潜在的赔付,因此零膨胀模型很常用。尽管在超额零数据建模方面取得了积极进展,但在零膨胀泊松模型中使用贝叶斯技术进行参数估计的方法尚未得到广泛探索。本研究旨在引入一种新的贝叶斯方法来估计零膨胀泊松模型的参数。该方法采用伽马和贝塔先验分布,推导出贝叶斯估计器和预测密度的封闭公式。此外,我们还提出了一种数据驱动方法,用于选择能产生高精度贝叶斯估计值的超参数值。模拟研究证实,对于小样本量和中等样本量,贝叶斯方法的准确性优于最大似然法(ML)。为了说明文章中提出的最大似然法和贝叶斯法,我们对一个真实数据集进行了分析。
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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 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.
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来源期刊
Risks
Risks Economics, Econometrics and Finance-Economics, Econometrics and Finance (miscellaneous)
CiteScore
3.80
自引率
22.70%
发文量
205
审稿时长
11 weeks
期刊最新文献
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