A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking
Bivariate Poisson regression models for ratemaking in car insurance have been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivaria...
| Authors: | , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/106474 |
| Online Access: | https://hdl.handle.net/2445/106474 |
| Access Level: | Open access |
| Keyword: | Inflació Anàlisi de regressió Assegurances d'accidents Variables (Matemàtica) Inflation Regression analysis Accident insurance Variables (Mathematics) |
| Summary: | Bivariate Poisson regression models for ratemaking in car insurance have been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivariate Poisson regression models is used to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, it is shown that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Finally, an EM algorithm is provided in order to ensure the models' ease-of-fit. These models are applied to an automobile insurance claims data set and it is shown that the modeling of the data set can be improved considerably. |
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