Functional Limit Theorems for Extreme Values of Arrays of Independent Random Variables
Functional Limit Theorems for Extreme Values of Arrays of Independent Random Variables
For an array $\{X_{ni}\}$ of independent, uniformly null random variables, several necessary and sufficient conditions are given for the convergence in distribution of its extremal process $\mathbf{M}_n = (M^1_n, M^2_n, \cdots)$ as $n \rightarrow \infty$, where $M^k_n(t) = k$th largest $\{X_{ni}: i/n \leq t\}, t > 0$. It is shown …