 Let formula_1 be a sequence of independent and identically-distributed random variables, and formula_2.If a sequence of pairs of real numbers formula_3 exists such that each formula_4 and
formula_5,
where formula_6 is a non-degenerate distribution function, then the limit distribution formula_6 belongs to either the Gumbel, the Fréchet or the Weibull family.These can be grouped into the generalized extreme value distribution.