A note on equal distributions
For each \(n\geq 1\), let \(X_{1,n}\leq X_{2,n}\leq...\leq X_{n,n}\) denote the ordered observations based on a random sample of size n from an arbitrary probability distribution F with finite mean. \textit{W. Hoeffding} [Ann. Math. Stat. 24, 93-100 (1953; Zbl 0050.136)] showed that the sequence \(\{E(X_{k,n}):1\leq k\leq n\), \(n\geq 1\}\) determines F. More recently, \textit{M. Pollak} [Ann. Stat. 1, 180-182 (1973; Zbl 0263.62008)] has given an improved version of Hoeffding's result. In the present note, Hoeffding's result is improved further.
scientific article; zbMATH DE number 3936176