13. A Simulation Study on Generalized Pareto Mixture Model

The Generalized Pareto Distribution is commonly used for extreme value problems. Especially, the values which exceed the finite threshold, is the focus in extreme value problems like in insurance sector. The Generalized Pareto Distribution is well approach for modeling the samples which include these extreme values. In the real life, samples are heterogeneous. In such cases, the mixture models are better way for modeling the data. In this study, we generate random samples from the Generalized Pareto Mixture Distribution for modeling of heterogeneous data. For this purpose, we use two different Generalized Pareto Distribution as components of the Generalized Pareto Mixture Distribution. For generating random samples, The Inverse Transformation Method is used in the simulation study. The parameters of the mixture models are shape, scale and location are fixed. After generating random samples, Chi-Square Goodness-of-Fit Test is used for checking whether the generated samples are distributed based on the Generalized Pareto Distribution. R-Statistical Programming Language is used in simulation study.