MODELLING NUMBER OF CLAIMS DATA IN PROPERTY INSURANCE USING ZERO INFLATED POISSON (ZIP) AUTOREGRESSION WITH LOCATION EFFECT - Urfina Zulkifli, Dhea
In insurance, it is interesting to know number of claims at a location that is observed from time to time. For claim that rarely happens, the amount of zero value is often found in the data, so the data’s variance is greater than the average. Generally, the number of events (count data) is modelled by the Poisson distribution. However, when the data’s variance is greater than the average, the Poisson distribution can’t be used anymore. One of alternatives that can be used is the Zero Inflated Poisson (ZIP) distribution. To build a ZIP Autoregression model that relies on the number of previous claims, the Generalized Linear Model is used. The influence of location is added to the regressor to determine the effect of the number of events on the surrounding neighbours towards the number of events at the location that is being analysed. The location effect is added with uniform and inverse distance squared weight. In uniform weight, each neighbour has the same effect on number of claims at the location that is being analysed. For the inverse distance squared weight, the closer the neighbour location is to the location of the area that is being analysed, the greater the inverse distance squared weighted. Modelling is done by giving the effect to the indicator function of number of claims in the previous time and number of claims in the previous time. In addition, predicted number of claims in the future is made and compared with the original data. The application of this data is used in the number of daily claim data of a property insurance company in 2010-2016 in Bekasi, Bogor, Depok, and Karawang. In this study, it is found that the model that is not influenced by the number of claims in the previous time is the best model. In addition, the model that is given the influence of the indicator function of number of claims in the previous time is better than the model that is given the influence of the number of claims in the previous time.