A mathematical model for grouped extreme values with an application in automotive engineering
This doctoral thesis presents a mathematical model for analyzing grouped data based on extreme values. Grouped data means that the exact outcome of the corresponding experiment is not known in detail, but only the occurrence frequency of the outcomes within a particular range or interval is given. In particular, the underlying experiment yields extreme values. In addition, the independent realizations of this experiment are all based on different observation periods. By dint of extreme value theory and the theory concerning count data, parametric models with regard to the number of events per time unit and domain are developed and analyzed. These models apply to real data from automotive industry.