National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Non-homogeneous Poisson process - estimation and simulation
Vedyushenko, Anna ; Pešta, Michal (advisor) ; Pawlas, Zbyněk (referee)
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
Archimedean copulas
Vedyushenko, Anna ; Pešta, Michal (advisor) ; Omelka, Marek (referee)
The thesis deals with Archimedean copulas which are very popular nowadays due to easy construction and their appealing properties. At first it introduces the general definition of a copula and also shows its fundamental properties. After that the definition and the basic properties of an Archimedean copula are discussed. The paper also describes some of the commonly used families of Archi- medean copulas. Then several methods of parameter estimation for Archimedean copulas are shown. Finally, we make a study of two real datasets where the distri- bution of the data is estimated based on the procedures described in the thesis. 1

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