Abstract
Let $F_n(x)$ denote the empirical distribution function of a random sample of size $n$ drawn from a population having continuous distribution function $F(x)$. In Section 3 the limiting distribution of the supremum of the random variables $\{F_n(x) - F(x)\}/F_n(x), |F_n(x) - F(x)|/F_n(x), \{F_n(x) - F(x)\}/(1 - F(x)), |F_n(x) - F(x)|/(1 - F(x)), \{F_n(x) - F(x)\}/(1 - F_n(x)), |F_n(x) - F(x))|/(1 - F_n(x))$ is derived where sup is taken over suitable ranges of $x$ respectively. Relevant tests and some combinations of them are also discussed briefly in Section 3.
Citation
Miklos Csorgo. "Some Renyi Type Limit Theorems for Empirical Distribution Functions." Ann. Math. Statist. 36 (1) 322 - 326, February, 1965. https://doi.org/10.1214/aoms/1177700296
Information