Document Type : Original Research Paper

Authors

• F. Salavati
• E. Bahrami Samani

Department of Insurance Statistics, Shahid Beheshti University, Tehran, Iran

Abstract

In third-party insurance, due to the reward-penalty system and the use of the end-of-year bonus system, the insured does not report his small losses to the insurance company. This creates many zeros in the number of claims for the insured. On the other hand, it is important for insurance companies to analyze the number of claims and the risk factors on this answer. For this purpose, some models with count responses using power series distribution such as Poisson regression model and negative binomial regression model and zero-accumulated power series distribution such as zero-accumulated Poisson regression model and zero-accumulated negative binomial regression for third-party insurance data analysis It is used with many zeros. In this paper, these models can be generalized to longitudinal third-party insurance data with a large number of zeros. A likelihood-based approach is used to obtain model parameter estimates. In this method, the EM algorithm is also used to estimate the parameters for models with zero accumulated response. Finally, to explain the usefulness of the proposed models, real longitudinal data of third party insurance has been analyzed.

Keywords

• EM-algorithm‎
• Third Party Liability Insurance
• No. of Claims
• ‎Zero- Inflated Distribution‎
• L‎ongitudinal ‎R‎esponses