The article considers application of the Kaniadakis' κ-statistics [1-3] (non-extensive statistical mechanics) which introduced in 2001 in the framework of Einstein's special theory of relativity, to the analysis and adequate description of extreme wind loads. The κ-deformed Kaniadakis exponential function is used to introduce new classes of κ-deformed statistical versions of known distributions. These distributions coincide with the original ones with the exception that their κ-deformed tail follows the Pareto power law. This allows converting the original distributions into heavy-tailed distributions that more closely match the experimental data of mixed systems and systems operating under conditions of increased uncertainty. This allows, within the framework of known distributions of loads and impacts, to model above-standard stressors and analyze the near impossible to predict “Black Swan” and “Dragon-King” ultra-rare type of events with humongous consequences.