On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth

Mergane, Pape Djiby; Lo, Gane Samb

doi:10.4236/am.2013.47136

Cited by 3 publications

(5 citation statements)

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“…[1−5]). Recently, [6] gathered a significant number of inequality measures under the name of Theil-like family. Such inequality measures are very important in capturing inequality in income distributions.…”

Section: Introductionmentioning

confidence: 99%

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

Kpanzou¹,

Ba²,

Mergane³

et al. 2019

JSTA

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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 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.

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Section: Introductionmentioning

confidence: 99%

“…Fortunately, [6] introduced the so-called Theil-like family, in which are gathered the Generalized Entropy Measure, the MDL [17−19], the different inequality measures of Atkinson [20], Champernowne [21] and Kolm [22] in the following form:…”

Section: Introductionmentioning

confidence: 99%

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

Kpanzou¹,

Ba²,

Mergane³

et al. 2019

JSTA

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“…Details on the definitions of inequality measures as well as non parametric estimators can be found in, e.g., Cowell and Flachaire (2007), Langel and Tillé (2011), Kpanzou (2011), Kpanzou (2014) and Kpanzou (2015). Further on inequality and poverty measures can be found in Lo (2013) and Lo and Mergane (2013). Kpanzou (2011) has developed semi-parametric estimators for measures of inequality and showed that these are very appropriate especially for heavy tailed distributions.…”

Section: Introductionmentioning

confidence: 99%

Measuring inequality: application of semi-parametric methods to real life data

Kpanzou¹,

Wet²,

Lo³

2017

AJAS

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Abstract. A number of methods have been introduced in order to measure the inequality in various situations such as income and expenditure. In order to curry out statistical inference, one often needs to estimate the available measures of inequality. Many estimators are available in the literature, the most used ones being the non parametric estimators. Kpanzou (2011) has developed semi-parametric estimators for measures of inequality and showed that these are very appropriate especially for heavy tailed distributions. In this paper we apply such semi-parametric methods to a practical data set and show how they compare to the non parametric estimators. A guidance is also given on the choice of parametric distributions to fit in the tails of the data. 158Résumé. Des méthodes ontété introduites en vue de mesurer l'inégalité dans diverses situations comme, par exemple, dans la répartition du revenu. Pour faire de l'inférence statistique, l'on a souvent besoin d'estimer les mesures d'inégalité disponibles. Des estimateurs ontété developpés, les plus utilisésétant les estimateurs non paramétriques. Kpanzou (2011) a developpé des estimateurs semi-paramétriques, estimateurs qui sont beaucoup plus appropriés surtout quand l'on aà traiter avec les distributionsà queueépaisse. Dans cet article, nous appliquons ces estimateurs semi-paramétriquesà des données de la vie réelle et les comparonsà leurséquivalents non paramétriques. Une indication est aussi donnée sur le choix des distributions paramétriquesà ajusterà la queue.

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“…But, we used to apply the our findings on real data from Households databases from from Senegal, Mali and Mauritania (See for example : Lo(2008), al. (2009), Lo(2013), Mergane and LO(2013), , Haidara and Lo(2013)).Here, we want to introduce simple methods on handling the databases before undertaking statistical procedures. we hope that this may help and encourage others to acquire the databases and get involved in the study of such treasures.…”

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VB and R codes using Households databases available in the NSI's : A prelude to statistical applied studies

Lo¹

2016

AJAS

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Abstract. We describe the main features of the households databases we can find in most of our National Statistics Institute. We provide algorithms aimed at extracting a diversity of variables on which different statistical procedures may be applied. Here, we particularly focus on the scaled income, as a beginning. Associated codes (MS Visual Basic ™ and R codes) have been successfully tested and delivered in the text and in a separate file.Résumé. Nous décrivons les principales caractéristiques des bases de données sur les ménages que nous pouvons trouver dans la plupart de nos Instituts Nationaux de Statistiques (INS). Nous fournissons des algorithmes visantà extraire une diversité de variables quantitatives ou qualitatives sur lesquelles différentes procédures statistiques peuventêtre appliquées. Ici, nous traitons entre autres de la variable revenu pondérée par l'échelle d'équivalence adulte, pour un début. Des codes correspondants (dans MS Visual Basic ™ et dans R) ont eté testés avec succés et sont fournis dans le texte et dans un fichier séparé.Key words: National Statistical Institutes (NSI); Preludes to Statistical Studies; Data storing; Data handling; Households databases; Algorithms; computer programs and codes. AMS 2010 Mathematics Subject Classification : 68P01; 68P05; 68N01Presented by Dr Diakarya Barro, Université Ouaga I Joseph Ki-Zerbo Corresponding Member of the Editorial Board * Corresponding author : gane-samb.lo@ugb.edu.sn, gslo@aust.edu.ng G.S. Lo, African Journal of Applied Statistics, Vol. 3 (1), 2016, pages 121 -156. VB™ and R codes using Households databases : A prelude to statistical applied studies. 122 IntroductionIn this paper, we want to share our experience in using some household databases one can find in most of African National Statistical institutes (NSI ).In most of the African countries, a number of surveys have been and continue to be conducted at a national wide level. The African Statistical Yearbook(2016), provided by the website of the African Center for Statistics ACS, uses data from 54 African countries. So, at the continental level, the availability of such households databases amounts to a considerable number of interesting and useful data collections. At the same time, it is very strange and disappointing that only a very few number of research works has been undertaken by African Scholars, at least, scholars in the Mathematics and Statistics Departments.As mentioned in LO(2014), I witnessed, as editor of Afrika Statistika for almost a decade and as a member of a number of Master and PhD theses juries, that most of our colleagues and our students use data sets concerning western countries and picked out from the books to illustrate their theoretical works. I reviewed a very interesting PhD thesis, from Central Africa, on Generalized Poisson Laws in which the candidate used data from England, exactly the number rain days in London. In my report, I pointed out such statistics do exist in meteorology stations and I recommended to contact them and to get the data.The e...

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On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth

Cited by 3 publications

References 21 publications

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

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

Measuring inequality: application of semi-parametric methods to real life data

VB and R codes using Households databases available in the NSI's : A prelude to statistical applied studies

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