Hall of Mirrors
Modeling the Tail of Finite Mixtures with Extreme Value Theory: Burr and Inverse Burr Distributions (304937)
*Leiyue Li, Miami UniversityMilan Jovanovic, University of Belgrade
Tatjana Miljkovic, Miami University
Keywords: Danish Fire, EVT, Frechet distribution, GPD, finite mixtures
Recent research on modeling heavy tailed insurance losses indicated that the mixture models based on Burr, Inverse Burr component distributions perform well in modeling heavy tail insurance loss data. Mixture models are able to capture the multimodality which is quite a common characteristic of insurance losses. The best fit for highly skewed Danish Fire losses is obtained with 2-component Burr and 3-component Inverse Burr mixture models. We show mathematically that these two mixtures belong to Maximum Domain of Attraction of Frechet distribution. Then, we study how 2-component Burr and 3-component Inverse Burr mixtures compare to Generalized Pareto Distribution (GPD) for modeling heavy tailed data. We estimate the confidence intervals and their coverage probability for the quantiles in the upper tail of these two mixtures using Order Statistics approach.