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dc.contributor.authorVladik Kreinovichen_US
dc.contributor.authorHung T. Nguyenen_US
dc.contributor.authorSongsak Sriboonchittaen_US
dc.contributor.authorOlga Koshelevaen_US
dc.description.abstract© Springer International Publishing AG 2017. In many real-life situations, a random quantity is a joint result of several independent factors, i.e., a sum of many independent random variables. The description of such sums is facilitated by the Central Limit Theorem, according to which, under reasonable conditions, the distribution of such a sum tends to normal. In several other situations, a random quantity is a maximum of several independent random variables. For such situations, there is also a limit theorem—the Extreme Value Theorem. However, the Extreme Value Theorem is only valid under the assumption that all the components are identically distributed—while no such assumption is needed for the Central Limit Theorem. Since in practice, the component distributions may be different, a natural question is: can we generalize the Extreme Value Theorem to a similar general case of possible different component distributions? In this paper, we use simple symmetries to prove that such a generalization is not possible. In other words, the task of modeling extremal events is provably more difficult than the task of modeling of joint effects of many factors.en_US
dc.subjectComputer Scienceen_US
dc.titleModeling extremal events is not easy: Why the extreme value theorem cannot be as general as the central limit theoremen_US
dc.typeBook Seriesen_US
article.title.sourcetitleStudies in Computational Intelligenceen_US
article.volume683en_US of Texas at El Pasoen_US Mexico State University Las Crucesen_US Mai Universityen_US
Appears in Collections:CMUL: Journal Articles

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