Generating Random Samples from the Generalized Pareto Mixture Model

The Generalized Pareto Distribution is a very useful tool for modeling in many areas of economics, finance and insurance. 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. Sometimes, intended samples might have a heterogeneous distribution. 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 three-parameters Generalized Pareto Distribution as components of the Generalized Pareto Mixture Distribution. For generating random samples, The Inverse Transformation Method is used in 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. Then, appropriate samples are combined for the determined mixture model with mixture weights. In simulation study, R-Statistical Programming Language is used.