1953/03/01 by Wassily Hoeffding
Mathematics · Physics and Astronomy · #Asymptotic distribution #Combinatorics #Distribution (mathematics) #Distribution function #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Moment (physics) #Noncentral chi-squared distribution #Order (exchange) #Order statistic #Physics #Quantum mechanics #Ratio distribution #Real line #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Statistics #Thermodynamics
paper · pdf · doi:10.1214/aoms/1177729086
openalex publication_date 1953/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
Let X1, X2, ⋯, Xn be independent with a common distribution function F(x) which has a finite mean, and let Zn1 \leqq Zn2 \leqq ⋯ \leqq Znn be the ordered values X1, ⋯, Xn. The distribution of the n values EZn1, ⋯, EZnn on the real line is studied for large n. In particular, it is shown that as n → ∞, the corresponding distribution function converges to F(x) and any moment of that distribution converges to the corresponding moment of F(x) if the latter exists. The distribution of the values Ef(Znm) for certain functions f(x) is also considered.