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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 Mergane and Lo (2013). On the other hand, the influence function of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analysed 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. † Tchilabalo Abozou Kpanzou (corresponding author). Kara University, Kara, Togo Email : kpanzout@gmail.com ††† Diam Ba LERSTAD, Gaston Berger University, Saint-Louis, Sénégal. Email : diamba79@gmail.com. †† Pape Djiby Mergane LERSTAD, Gaston Berger University, Saint-Louis, Sénégal. Email : mergane@gmail.com. †††† Gane Samb Lo. LERSTAD, Gaston Berger University, Saint-Louis, Sénégal (main affiliation). LSTA, Pierre and Marie Curie University, Paris VI, France. AUST African University of Sciences and Technology, Abuja, Nigeria gane-samb.lo@edu.ugb.sn, gslo@aust.edu.ng, ganesamblo@ganesamblo.net Permanent address : 1178 Evanston Dr NWT3P 0J9,Calgary, Alberta, Canada. keywords and phrases. Influence function, Measures of inequality, Lorenz curve, quantile function, Pareto law, Exponential law, Singh-Maddala law, lognormal law, . AMS 2010 Mathematics Subject Classification : 62G35, 97K70.

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