Fisher-Tippett-Gnedenko Theorem

The Fisher-Tippett-Gnedenko Theorem is a foundational result of extreme value theory describing the possible limiting behavior of the maximum of a large sample of independent, identically distributed random variables. It shows that, after proper rescaling, this maximum can only converge in distribution to one of three families of distributions: the Gumbel, the Frechet, or the Weibull distribution. Credit for the theorem is shared among Maurice Frechet, Ronald Fisher and Leonard Tippett, Richard von Mises, and Boris Gnedenko, whose work between the 1920s and 1943 established its full statement.