Asymptotic Theory of Extreme Order Statistics*

Let X ₁, X ₂,… be i.i.d. with continuous distribution function F(x) and let M _n denote the maximum of the first n observations, M _n = max _{j ≤ n} X _j. Then the distribution function of M _n is P(M _n ≤, x) = F(x) ⁿ .