Frequency Data Modeling of Passenger Transport Auto Insurance Claims Using the New Poisson Mixed Weighted Lindley Distribution
DOI:
https://doi.org/10.36456/jstat.vol18.no2.a10820Keywords:
Car Insurance, Claim Frequency, NPWL Distribution, OverdispersionAbstract
Vehicle insurance is an important instrument in risk management. However, claim frequency modeling often faces overdispersion issues, rendering the equidispersion assumption in Poisson distribution invalid. Alternative distributions such as Negative Binomial have been widely used to address this issue, but they still have limitations in capturing claim heterogeneity in some insurance data. This study applies the New Poisson Mixed Weighted Lindley (NPWL) distribution to passenger transport vehicle insurance claim frequency data in Indonesia sourced from PT. XYZ in the 2013 underwriting year. Parameter estimation was performed using the Maximum Likelihood approach, and model fit was evaluated using the Chi-Square test. The results show that the NPWL model provides a good fit to the data, with a Chi-Square test statistic value of 0.7341, which is smaller than the critical value. The parameter estimates obtained were 4.5919 and 0.8539, which resulted in a mean value of 0.3811 and a variance of 0.4033. The variance being greater than the mean indicates that NPWL is able to capture overdispersion more flexibly than the conventional Poisson model, making it more relevant for practical applications in setting vehicle insurance premiums.
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