On the rate of strong consistency of Lorenz curves

DOI10.1016/S0167-7152(97)82789-7zbMath0894.60031OpenAlexW2001587611MaRDI QIDQ1380637

Ričardas Zitikis, Miklós Csörgő

Publication date: 30 August 1998

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(97)82789-7

zbMATH Keywords

consistencylaw of the iterated logarithmempirical processLorenz curvequantile processLorenz processVervaat processintegrated Bahadur-Kiefer process

Mathematics Subject Classification ID

Strong limit theorems (60F15) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (10)

Lorenz curve for truncated and censored data ⋮ Composing the cumulative quantile regression function and the Goldie concentration curve ⋮ On the cumulative quantile regression process ⋮ Describing the concentration of income populations by functional principal component analysis on Lorenz curves ⋮ Concentration curve for truncated and censored data ⋮ Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution ⋮ Convex rearrangements of Lévy processes ⋮ Asymptotic Behaviors of the Lorenz Curve for Censored Data Under Strong Mixing ⋮ On the rate of strong consistency of the total time on test statistic ⋮ Asymptotic confidence bands for the Lorenz and Bonferroni curves based on the empirical Lorenz curve

Cites Work

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• An asymptotic theory for empirical reliability and concentration processes
• Strong approximations of the quantile process
• Strassen's LIL for the Lorenz curve
• Strassen's law of the iterated logarithm for the Lorenz curves
• The law of the iterated logarithm for normalized empirical distribution function
• Convergence theorems for empirical Lorenz curves and their inverses
• A Scale-Free Goddness-of-Fit Test for the Exponential Distribution Based on the Lorenz Curve
• A Note on Quantiles in Large Samples
• On Bahadur's Representation of Sample Quantiles
• Functional central limit theorems for processes with positive drift and their inverses
• A General Definition of the Lorenz Curve

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