Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity

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