Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity

This paper deals with the extreme value analysis for the triangular arrays which appear when some parameters of the mixture model vary as the number of observations grows. When the mixing parameter is small, it is natural to associate one of the components with an impurity (in the case of regularly varying distribution, heavy-tailed impurity), which pollutes another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher-Tippett-Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.

Automated summary

This paper discusses extreme value analysis for triangular arrays in mixture models where parameters vary with increasing observations. It introduces a new model for studying maximal stock returns values and demonstrates its effectiveness with numerical examples.