On the Influence Function for the Theil-Like Class of Inequality Measures

On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986–1000. On the other hand, the influence function (IF) of statistics is an important tool in the...

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Bibliographic Details
Published in:Journal of Statistical Theory and Applications (JSTA) 2019-09, Vol.18 (3), p.270-277
Main Authors: Kpanzou, Tchilabalo Abozou, Ba, Diam, Mergane, Pape Djiby, Lo, Gane Samb
Format: Article
Language:English
Subjects:
Comparative studies
Inequality measures
Influence function
Influence functions
Lorenz curve
Measures of inequality
Quantile function
Research Article
Theil
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Summary:On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986–1000. On the other hand, the influence function (IF) of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analyzed in various aspects for a large number of statistics. We proceed to a unifying study of the IF of all the members of the so-called Theil-like family and regroup those IF ’s in one formula. Comparative studies become easier.
ISSN:1538-7887
2214-1766
DOI:10.2991/jsta.d.190818.002