Μοντέλα πιθανοτήτων για περιγραφή δεδομένων κίνδυνων
Probability models for fitting risk data
It is common knowledge that there are many features that cannot be described fully by traditional distributions such as the normal or the exponential one. Such typical cases are either the yield of an investment or the amount of compensation of an insurance company, which exhibit extreme values. Dealing with this kind of data, classical statistical models are insufficient in analysis. This thesis deals with generalized beta generated (GBG) class of distributions which extends several common distributions, called parent generators, into distributions characterized by their flexibility in modeling data in practice. The study has the following structure. The first chapter is an introductory section regarding the basic characteristics of normal distribution making it an attractive tool for studying hazards in general. Also the need for development models that are suitable to formulate the abovementioned data is discussed. The second chapter refers to distributions models that have been proposed to approach the non-normal data, namely the transformed beta family and the beta generated class of distributions. Subsequently, the GBG class of distributions is analyzed thoroughly and its basic statistical measures are presented as well. In chapter three, the results obtained by the analysis performed in chapter two are specified using as parent distributions the Pareto, the Weibull and the Logistic distributions. In each case, the distribution of the parent is analyzed in details and the corresponding GBG distribution with its own characteristics is provided. The fourth chapter investigates the flexibility and applicability of GBG distributions in modeling a set of real data. Finally, the appendix provides the definitions and relevant properties of Gamma and Beta functions, and considers the proofs that have not been detailed in the main body of this study.