Journal ArticleDOI
On statistical inference in concentration measurement
TLDR
In this article, the asymptotic distribution for a certain class of functionals of distribution functions is derived, and the results are applied to the Lorenz-curve and the Gini-measure as special cases of the abovementioned functionals.Abstract:
The asymptotic distribution for a certain class of functionals of distribution functions is derived. This result is used to give distribution free asymptotic confidence intervals for these functionals; for this purpose, a strongly consistent estimate for the asymptotic variance is constructed. These results are applied to the Lorenz-curve and the Gini-measure as special cases of the abovementioned class of functionals.read more
Citations
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Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Book
Statistical Size Distributions in Economics and Actuarial Sciences
Christian Kleiber,Samuel Kotz +1 more
TL;DR: The Statistical Size Distribution in Economics and Actuarial Sciences (SDFIS) as discussed by the authors is a collection of parametric models that deal with income, wealth, and related notions.
Journal ArticleDOI
Distribution-Free Statistical Inference with Lorenz Curves and Income Shares
TL;DR: In this article, the authors considered the problem of statistical inference with estimated Lorenz curves and income shares and derived the full variance-covariance structure of the (asymptotic) normal distribution of a vector of Lorenz curve ordinates.
Journal ArticleDOI
A note on pro-poor growth
TL;DR: In this paper, the authors proposed a "poverty growth curve" that measures whether economic growth is pro-poor or not propoor, based on Atkinson's theorem linking the generalized Lorenz curve and changes in poverty.
Journal ArticleDOI
Calculating a Standard Error for the Gini Coefficient: Some Further Results*
TL;DR: In this paper, it was shown that obtaining an exact analytical expression for the standard error is actually a trivial matter and that several interesting hypotheses regarding the sensitivity of the Gini coefficient to changes in the data are readily tested in a formal manner.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
Functions of Order Statistics
TL;DR: Two theorems on the asymptotic normality of linear combinations of functions of order statistics are given in this article, one requires a smooth scoring function but the underlying df need not be continuous even and can also depend on the sample size.
Journal ArticleDOI
A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics
TL;DR: A strengthened version of the Glivenko-Cantelli theorem for the uniform empirical distribution function is proved in this article, which is used to establish strong laws of large numbers for linear functions of order statistics.
Journal ArticleDOI
Einige Bemerkungen zur statistischen Messung der Konzentration
TL;DR: In this article, einige kritischen Analyse der Begriffe „absolute“ and „relative“ Konzentration werden gegeben, die Maszahlen der absoluten oder der relativen KonzENTration zu erfullen haben.