This thesis covers non-homogeneous Poisson processes along with estimation of the intensity (rate) function and some selected simulation methods. In Chapter 1 the main properties of a non-homogeneous Poisson process are summarized. The main focus of Chapter 2 is the general maximum likelihood estimation procedure adjusted to a non-homogeneous Poisson process, together with some recommen- dations about calculation of the initial estimates of the intensity function param- eters. In Chapter 3 some general simulation methods as well as the methods designed specially for log linear and log quadratic rate functions are discussed. Chapter 4 contains the application of the described estimation and simulation methods on real data from non-life insurance. Furthermore, the considered sim- ulation methods are compared with respect to their time efficiency and accuracy of the simulations. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:386960 |
| Date | January 2018 |
| Creators | Vedyushenko, Anna |
| Contributors | Pešta, Michal, Pawlas, Zbyněk |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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