= Extremal types theorem
= Fisher–Tippett–Gnedenko theorem
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{synonym}
Every non-degenerate limit in <convergence in distribution> of positively scaled and centered <sample maxima> is a <max-stable distribution>. Up to positive affine transformations its law is the <Gumbel distribution>, a <Fréchet distribution> with positive shape parameter, or a <negative Weibull distribution> with positive shape parameter. This classifies possible limits, without asserting that every <distribution function> admits a limiting normalization.
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