Skip to main content
Article thumbnail
Location of Repository

Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution

By V. Fakoor, M. Bolbolian Ghalibaf and H.A. Azarnoosh


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.Gini index Length-biased distribution Lorenz curve Strong consistency Strong Gaussian approximation

OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.