Title : ( Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution )
Authors: Vahid Fakoor , Mohammad Bolbolian Ghalibaf , Hassan Ali Azarnoosh ,
Full TextAbstract
In this work, we consider the nonparametric estimators of the Lorenz curve and Gini index based on a sample from the corresponding length-biased distribution. We show that this estimators are strongly consistent for the associated Lorenz curve and Gini index. Strong Gaussian approximations for the associated Lorenz process are established under appropriate assumptions. We apply the strong Gaussian approximation technique to obtain a functional law for the iterated logarithm for the Lorenz curve. Also, we obtain an asymptotic normality for the corresponding Gini index
Keywords
, Gini index Length, biased distribution Lorenz curve Strong consistency Strong Gaussian approximation
@article{paperid:1022141,
author = {Fakoor, Vahid and Bolbolian Ghalibaf, Mohammad and Azarnoosh, Hassan Ali},
title = {Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution},
journal = {Statistics and Probability Letters},
year = {2011},
volume = {81},
number = {9},
month = {September},
issn = {0167-7152},
pages = {1425--1435},
numpages = {10},
keywords = {Gini index
Length-biased distribution
Lorenz curve
Strong consistency
Strong Gaussian approximation},
}
%0 Journal Article
%T Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution
%A Fakoor, Vahid
%A Bolbolian Ghalibaf, Mohammad
%A Azarnoosh, Hassan Ali
%J Statistics and Probability Letters
%@ 0167-7152
%D 2011
