Open Access
VOL. 1 | 2018 Chapter 10. On the joint distribution of variations of the Gini index and Welfare indices
Pape Djiby MERGANE, Gane Samb LO, Tchilabalo Abozou KPANZOU

Editor(s) Hamet SEYDI, Gane Samb LO, Aboubakary DIAKHABY


The aim of this paper is to establish the asymptotic behavior of the mutual influence of the Gini index and the poverty measures by using the Gaussian fields described in Mergane (2013). The results are given as representation theorems using the Gaussian fields of the unidimensional or the bidimensional functional Brownian bridges. Such representations, when combined with those already available, lead to joint asymptotic distributions with other statistics of interest like growth, welfare and inequality indices and then, unveil interesting results related to the mutual influence between them. The results are also appropriate for studying whether a growth is fair or not, depending on the variation of the inequality measure. Data driven applications are also available. Although the variances may seem complicated at a first sight, their computations which are needed to get confidence intervals of the indices, are possible with the help of R software. Beyond the current results, the provided representations are useful in connection with different ones of other statistics.


Published: 1 January 2018
First available in Project Euclid: 26 September 2019

Digital Object Identifier: 10.16929/sbs/2018.100-02-07

Primary: 60F05 , 60F17 , 91B82 , 91C05

Keywords: asymptotic normality , functional empirical process , Gaussian processes and fields , general poverty measures , Gini's index , pro and anti-poor growth , weak laws , welfare and inequality measure

Rights: Copyright © 2018 The Statistics and Probability African Society

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