Extremal types theorem

{title2=$F(a_nx+b_n)^n=F(x)$}

= Max-stable
{synonym}

A non-degenerate <distribution function> is max-stable when every <sample maximum> of $n$ <independent and identically distributed random variables> can be positively scaled and centered to have the original law. Thus for every integer $n\geq1$ there are $a_n>0,b_n\in\mathbb R$ with $F(a_nx+b_n)^n=F(x)$. The <extremal types theorem> classifies these laws, up to affine changes, as the <Gumbel distribution>, <Fréchet distribution>, and <negative Weibull distribution>.


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 Incoming links: Max-stable distribution