The article considers application of the Kaniadakis’ κ-statistics (non-extensive statistical mechanics introduced by C. Tsallis in 1988, is presented in relation with the q-triplet estimation concerning experimental time series from climate, seismogenesis, and space plasmas systems), which appeared in 2001 in the framework of Einstein's special theory of relativity, to description of loads and impacts on buildings and structures. The κ-deformed Kaniadakis exponential function is used, with the help of which new classes of κ-deformed statistical versions of already known distributions are introduced. 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 the already known distributions of loads and impacts, to model above-standard stressors and analyze the near impossible to predict “Black Swan” ultra rare type of events with humongous consequences.