Extreme Value Distributions

Abstract

Extreme value distributions arise in probability theory as limit distributions of maximum or minimum of n independent and identically distributed random variables with some normalizing constants For example if $\text {X}_{1,} \text {X}_{2}, {\ldots }, \text {X}_\mathrm{{n}}$ are n independent and identically distributed random variables, then the largest normalized order statistic $\text {X}_\mathrm{{n,n,}}$ will converge to one of the following three distributions if it has a nondegenerate distribution as $\text {n}\rightarrow \infty$.