See Fisher-Tippett-Gnedenko theorem on Wiktionary
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"A general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of three possible distribution families: the Gumbel distribution, the Fréchet distribution, or the Weibull distribution."
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"(statistics) A general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of three possible distribution families: the Gumbel distribution, the Fréchet distribution, or the Weibull distribution."
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