| Abstract [eng] |
The subject of the research is statistical analysis of claim arrival times and claim sizes in non-life insurance. First, I present some standard models and tools of non-life insurance mathematics. Also, I introduce the statistical tools for analysing the claim number and size processes, such as QQ plots, Mean excess plots, etc. Second, the statistical analysis of claim arrival times and claim sizes for the 4 years real car insurance data are done. Results show that homogeneous Poisson process is a suitable model for the arrivals for shorter periods of time (such as one year). In addition, claim sizes data reveals heavy-tailedness and skewedness to the right. Finally, the change point problem in the rate parameter of the Poisson process was studied. The change point was detected using algorithm given in [2]. |
