Canadian Journal of Statistics

Limiting distributions of Kolmogorov‐Lévy‐type statistics under the alternative

Journal Article


Let Xi, 1 ≤ in, be independent identically distributed random variables with a common distribution function F, and let G be a smooth distribution function. We derive the limit distribution of α(Fn, G) ‐ α(F, G)}, where Fn is the empirical distribution function based on X1,…,Xn and α is a Kolmogorov‐Lévy‐type metric between distribution functions. For α ≤ 0 and two distribution functions F and G the metric pα is given by pα(F, G) = inf {ϵ ≤ 0: G(x ‐ αϵ) ‐ ϵ F(x)G(x + αϵ) + ϵ for all x ℝ}.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.