| Statistical inference |
| Written by theoretic |
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Although statistical inference on the processes S and N is utterly important for the insurance business, we do not address this aspect in a rigorous way. The statistical analysis of insurance data is not different from standard statistical methods which have been developed for iid data and for counting processes. Whereas there exist numerous monographs dealing with the inference of iid data, books on the inference of counting processes are perhaps less known. We refer to the book by Andersen et al. [2] for a comprehensive treatment. We start with the extensive Chapter 2 on the modeling of the claim number process N. The process of main interest is the Poisson process. It is treated in Section 2.1. The Poisson process has various attractive theoretical properties which have been collected for several decades. Therefore it is not surprising that it made its way into insurance mathematics from the very beginning, starting with Lundberg’s thesis [55]. Although the Poisson process is perhaps not the most realistic process when it comes to fitting real-life claim arrival times, it is kind of a benchmark process. Other models for N are modifications of the Poisson process which yield greater flexibility in one way or the other. |