Hypernormal distribution theory: Analysis of the set of extreme random variables models

The analysis of the set of extreme random variables models is still an extremely topical topic in many areas of mathematical research in the theory and practice of managing production processes due to its specificity and great interest in finding an expectation and stability indicators set studied in practical economics. Calculations of applied mathematics help to determine tentatively possible boundary parameters of various models, i.e., expectations, despite the fact that theoretical calculations do not have a direct association with practical data. Nevertheless, the consideration of extreme models of extreme random variables is still relevant in many areas of science and industry. The study subject was the hypernormal distribution theory. The study object was a set of extreme random variables models. The study purpose was a comprehensive analysis of many models of extreme random variables. To achieve the purpose and solve the tasks formulated on its basis, empirical, analytical and comparative methods of data analysis and the method of mathematical modelling, which contributed to the study of the materials presented in this article, were used. In the study course, materials from the works of such leading world experts in extreme value theory and programming K. Beck, M. Fowler, L. Tippett, E. Gumbel, K. Auer, R. Miller, and Scott W. Ambler and researchers as V.L. Khatskevich, B.V. Gnedenko, V.A. Akimov, V.A. Bykov, E.Yu. Shchetinin, K.M. Nazarenko, L.P. Kvashko, A.S. Losev, V.S. Mikhailov, V.A. Popov, E.R. Smolyakov. In the study course, the definition of an extreme value within the framework of the theory was refined, the typology of the distribution of maximum values was analysed, seven theories of the hypernormal distribution were identified and their proofs were presented, and practical examples of the application of each theory were given. The practical significance of the study of extreme random variables models in various areas of industrial human activity was confirmed. The materials of the study can be used in the widest range: from application in risk management of industrial production to predicting the probabilities of natural phenomena, which makes it possible to prevent significant economic and social losses of society, as well as make a tangible contribution to programming the probabilities of the development of the society of the future.