Tarptautinių atsiskaitymų banko (BIS) Bazelio II susitarimo nuostatos dėl bankų minimalaus kapitalo apibrėžia reikalavimus kredito rizikos skaičiavimui. Kredito rizikos vertinimo metodai leidžia naudoti vidines įmonių reitingavimo sistemas. Vienas svarbiausių reitingavimo modelio uždavinių – į modelį parinkti tokius finansinius ar nefinansinius rodiklius, kurie geriausiai klasifikuotų įmones pagal jų finansinio pajėgumo lygį. Populiariausias statistinis atrankos rodiklis yra tikslumo koeficientas dar vadinamas Gini indeksu. Tradicinis Gini indeksas buvo apibrėžtas 1914 m. ir iki šiol yra naudojamas pajamų nelygybei populiacijoje apskaičiuoti. 1995 m. Mosleris ir Koševojus pristatė k-matį Gini indekso analogą kaip zonoido tūrį. Šio darbo tikslas – naudojantis zonoidų teorijos idėjomis sukonstruoti apibendrintą reitingavimo modelių Gini indeksą. Pirmoje darbo dalyje pateiktos tradicinės Lorenco kreivės bei Gini indekso sąvokos ir Gini indekso apibendrinimai. Antroje darbo dalyje pagal BIS naudojamas reitingavimo modelio galios sąvokas, apibrėžtas reitingavimo modelio Gini indeksas. Be to, apibrėžti Lorenco kreivės apatinės ir viršutinės aproksimacijų Gini indeksai bei sudaryti šių indeksų apibendrinimai – normos bei tūrio daugiamačiai Gini indeksai. Pabaigoje analizuojamas atskirų finansinių rodiklių Gini indeksų stabilumas bei bendras Gini indeksų – vienamčio, normos ir tūrio – stabilumas ir pateikiamos išvados. / Bank for International Settlements (BIS) Basel II resolutions on banks regulatory capital include requirements for credit risk calculation. Credit risk evaluation methods define the possibility of using the internal rating system. One of the main tasks to build the powerful scoring model is to select financial and non-financial factors that appropriately classify companies according to their financial situation. The most popular statistical measure used for discriminatory analysis is the accuracy ratio or Gini index. General Gini index presented in 1914 is still widely applied to measure income inequality in the population. The k-dimensional analogue of Gini index as volume of zonoid was defined only in 1995 by Mosler and Koshevoy. The main purpose of this paper is to build the generalized Gini index of scoring model following the theory of zonoids. In the first part of the paper the usual Lorenz curve, traditional Gini index and its summary measures are presented. The second part presents the definition of the scoring models Gini index according to scoring model power measures applied in BIS resolutions. Furthermore the Gini indexes of Lorenz curve bottom and top approximations are defined and two its summary measures – norm and volume Gini indexes are constructed. Finally the stability of separate financial ratios Gini indexes and the general stability of univariate, norm and volume Gini indexes are analysed and final conclusions are presented.

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1 Abstract Title: Dynamic competitive balance in European football leagues Objectives The quality of objective of this master thesis is the analysis of dynamic competitive balance of ten European football leagues. Namely the English league, the German league, the Dutch league, the Greek league, the Romanian league, the Czech league, the Danish league, the Polish league, the Cyprian league, the and the Bulgarian league and their comparison. Methods: Dynamic competitive balance showed by the Lorenz curve of the number of league champions during the period under review. Results: The results show comparison of dynamic competitive balance in top European leagues. Further refute or confirm the established assumption of same trend in the designated groups divided by market value and competitive format. Key words: Football, competition, dynamic balance, Lorenz curve, league market value, competitive format

Since its introduction by Max Otto Lorenz, the Lorenz curve has been utilizedin several financial contexts. By using regression analysis to approximate theclaim cost of policyholders, a vector consisting of policyholder characteristics canbe obtained. The ordered Lorenz curve can subsequently be used to understandwhat commonalities are shared between profitable policyholders. This allows forbetter management of the insurance portfolio and thus better customer relationstowards both the policyholders and the insurer, which is important for an insuranceconsultancy agency. The aim of this thesis was to investigate which attributesapproximate the policyholder claim costs and consequently obtain insight into whatattributes are shared among profitable portfolio clients. The results presented inthis thesis show that a multi-linear regression model, transformed using the Box-Cox method is insufficient to approximate the claim costs in a convincing manner.The model obtained in the thesis was capable of identifying significant regressorsbut the overall result displayed uncertainties in regards to overall goodness of fit.This means that the variability explained by the regression model only represents4.95% of the variability in the claim cost data. Thus, the relativity measureintroduced in section 2.1.1 was deemed uninterruptible in a meaningful way.Consequently, the empirical distribution functions presented in section 1.1 wouldbe based on a faulty order statistic, and in turn the visualization of an orderedLorenz curve with such a relativity measure is unnecessary. / Sedan Lorenzkurvan introducerades av Max Otto Lorenz 1904 har den använtsinom flera finansiella sammanhang. Genom att använda regressionsanalys föratt approximera försäkringstagares skadekostnader kan en vektor som består avförsäkringstagarnas attribut erhållas. Den sorterade Lorenzkurvan kan i sin turanvändas för att förstå vilka gemensamma attribut som delas mellan lönsammaförsäkringstagare. Detta möjliggör bättre hantering av försäkringsportföljen ochdärmed bättre kundrelationer mot både försäkringstagarna och försäkringsbolaget,något som är viktigt för försäkringsförmedlare. Syftet med denna avhandling var attundersöka vilka egenskaper som approximerar försäkringstagarnas skadekostnaderoch därmed få insikt i vilka attribut som delas bland lönsamma portföljkunder.Resultaten som presenteras i denna avhandling visar att en multilinjär regressionsmodell,som transformeras med Box-Cox-metoden, är otillräcklig för att approximeraskadekostnader på ett övertygande sätt. Modellen som erhölls i avhandlingenkunde identifiera signifikanta regressorer, men det övergripande resultatet visadeosäkerheter när det gäller den generella anpassning. Detta innebär att variabilitetensom förklaras av regressionsmodellen bara representerar 4,95% av variabilitetenbland skadekostnadsdatan. Därmed ansågs relativitetsmåttet som introduceras iavsnitt 2.1.1 vara oanvändbart på ett meningsfullt sätt. Följaktligen ger de empiriskafördelningsfunktionerna som presenteras i avsnitt 1.1 ett felaktig sorteringsmåttsom i sin tur medför att visualiseringen av en sorterad Lorenzkurva baserad påovannämnda mått är onödigt.

La notion de pauvreté a fait l’objet de nombreux débats à travers le monde. Les premières analyses ont mis l’accent sur le caractère unidimensionnel basé essentiellement sur une approche monétaire (revenu ou dépense de consommation). C’est à la faveur des travaux de certains auteurs, tels que Townsend et Sen, que le caractère multidimensionnel est mis en lumière, au regard de la difficulté de quantification de certaines variables qui traduisaient l’idée de manque. l ressort des nombreuses études empiriques que le secteur rural reste le secteur le plus touché par le phénomène de pauvreté.Dans le cas de la Côte d’Ivoire, la pauvreté reste également un phénomène rural et la plupart des études réalisées se sont focalisées sur l’approche monétaire. Cette étude aborde l’analyse de la pauvreté en se focalisant sur le milieu rural agricole et appréhende le phénomène de la pauvreté à partir de trois (03) approches : (i) monétaire ; (ii) privation relative et (iii) patrimoine.Les résultats montrent que la pauvreté reste importante dans ce secteur avec un taux plus élevé pour l’indicateur de privation relative. En outre, il existe une inégalité monétaire plus importante que les autres types de pauvreté quel que soit l’année (2002 et 2008).L’identification des facteurs explicatifs de l’appartenance ou non à la classe des pauvres, montre que les variables liées au genre, au type de religion et à la classe d’âge sont les plus communes aux différentes années et aux différentes approches.Sur la base des résultats obtenus, les recommandations suivantes sont formulées : (i) à l’endroit du gouvernement ivoirien, utiliser les approches monétaires et non-monétaires dans les prochaines analyses sur la pauvreté en Côte d’Ivoire ; mettre l’accent sur la construction de nouvelles infrastructures et l’achat de nouveaux équipements ; améliorer la communication relatives aux actions du gouvernement ; renforcer les capacités des producteurs en matière d’utilisation d’intrants améliorés et d’outils pertinents ; (ii) à l’endroit des producteurs agricoles, adopter les technologies et techniques agricoles et des intrants de qualité, accepter d’adhérer à des entreprises coopératives ; (iii) à l’endroit des coopératives, il faut rechercher des débouchés pour ses membres, négocier de meilleures rémunérations des productions agricoles, transformer les agriculteurs en véritables entrepreneurs agricoles. / The notion of poverty has been the subject of much debate around the world. Previous analyses have emphasized the one-dimensional character based essentially on a monetary approach (income or consumption expenditure). Thanks to the work of some authors such as Townsend and Sen, the multidimensional character is highlighted, considering the difficulty of quantifying certain variables that translated the idea of lack. In addition, many empirical studies show that the rural sector remains the most affected by poverty.In the case of Côte d'Ivoire, poverty is also a rural phenomenon and most studies have focused on the monetary approach.This study addresses the analysis of poverty by focusing on rural farming and apprehends the phenomenon of poverty from three (03) approaches: (i) monetary; (ii) relative deprivation and (iii) wealth.The results show that poverty remains important in this sector with a high rate for the indicator of the relative deprivation. In addition, there is greater monetary inequality than other types of poverty whatever the year (2002 and 2008).The identification of the explanatory factors of the membership or not in the class of the poor shows that the variables related to the gender, to the type of religion and the age group are the most common in the various years and various approaches.Based on the obtained results , the following recommendations are formulated: (i) towards the Ivorian government, use monetary and non-monetary approaches in next analyses on poverty in Côte d’Ivoire; emphasize the construction of new infrastructures and the purchase of new equipment; improve communication about government actions; build the capacity of producers to use improved inputs and relevant tools; (ii) to agricultural producers, adopt agricultural technologies and techniques and quality inputs, accept to join cooperative enterprises; (iii) for cooperatives, it is necessary to look for outlets for its members, to negotiate better remunerations for agricultural productions, to transform farmers into real agricultural entrepreneurs.

Thesis (Ph.D. (Economics))--North-West University, Vaal Triangle Campus, 2004.

This thesis studies the effects of specific community- driven developer programmes run in Evaton West over the past three years (200011 to 200314) on poverty in the area. These programmes were targeted at poverty reduction and community development in Evaton West, driven by the Eindhoven municipality and COL~AP~A'@. The relationship between the Eindhoven Municipality and the Ernfuleni Municipality started as a result of the twinning of Tilburg and Eindhoven cities in the Netherlands with the erstwhile LekoaNaal Local Metropolitan Council. Evaton West was chosen as a pilot site for Eindhoven to run practical IDP programmes at, as an example of what can be achieved from properly run community-based programmes. COL~AP~Aw' as introduced to Evaton West by the Vaal University of Technology's Community Service department. Its programmes were aimed at poverty alleviation through small-scale business initiatives coupled with leadership training in the area. The approach in the thesis is to define poverty, measure it and determine the profile of the poor. This is done firstly employing household-level indicators and secondly employing community-level indicators. At household level, some of the following tools are used: the poverty line (HSL), headcount index, the poverty gap, dependency ratio, the Lorenz curve and the Gini coefficient. Unemployment is also used to determine poverty levels. At community level, the thesis employs tools such as community characteristics, community assets, principal services, education, health and environmental issues. The thesis ends with specific recommendations. In particular, formation of co-operatives and the introduction of the basic income grant (BIG) are proposed. The thesis shows that compared to Bophelong, which is approximately similar to Evaton West in terms of age and composition of residents (especially based on age analysis), Evaton West is worse-off judging by poverty and welfare at household level. It proposes that one of the problems is Evaton West's geographical displacement. The thesis also shows that compared to three years ago, Evaton west is marginally better-off judging from the community indicators applied. It ascribed such improvement to the application of the above-stated community-driven development projects in Evaton West. Finally, the thesis suggests that one of the major solutions in dealing with poverty is to consider small-scale, home-based industries that allow for easy entry. Such projects can only succeed if they are approached in an integrated manner in which local authorities are fully involved. Labour absorption capacity of large industries is declining. This forces policy-making to be redirected to alternative sources of employment. The thesis contributes ways in which community-driven development programmes may be assessed at household and community levels. / Thesis (Ph.D. (Economics))--North-West University, Vaal Triangle Campus, 2004.

This thesis studies the effects of specific community- driven developer programmes run in Evaton West over the past three years (200011 to 200314) on poverty in the area. These programmes were targeted at poverty reduction and community development in Evaton West, driven by the Eindhoven municipality and COL~AP~A'@. The relationship between the Eindhoven Municipality and the Ernfuleni Municipality started as a result of the twinning of Tilburg and Eindhoven cities in the Netherlands with the erstwhile LekoaNaal Local Metropolitan Council. Evaton West was chosen as a pilot site for Eindhoven to run practical IDP programmes at, as an example of what can be achieved from properly run community-based programmes. COL~AP~Aw' as introduced to Evaton West by the Vaal University of Technology's Community Service department. Its programmes were aimed at poverty alleviation through small-scale business initiatives coupled with leadership training in the area. The approach in the thesis is to define poverty, measure it and determine the profile of the poor. This is done firstly employing household-level indicators and secondly employing community-level indicators. At household level, some of the following tools are used: the poverty line (HSL), headcount index, the poverty gap, dependency ratio, the Lorenz curve and the Gini coefficient. Unemployment is also used to determine poverty levels. At community level, the thesis employs tools such as community characteristics, community assets, principal services, education, health and environmental issues. The thesis ends with specific recommendations. In particular, formation of co-operatives and the introduction of the basic income grant (BIG) are proposed. The thesis shows that compared to Bophelong, which is approximately similar to Evaton West in terms of age and composition of residents (especially based on age analysis), Evaton West is worse-off judging by poverty and welfare at household level. It proposes that one of the problems is Evaton West's geographical displacement. The thesis also shows that compared to three years ago, Evaton west is marginally better-off judging from the community indicators applied. It ascribed such improvement to the application of the above-stated community-driven development projects in Evaton West. Finally, the thesis suggests that one of the major solutions in dealing with poverty is to consider small-scale, home-based industries that allow for easy entry. Such projects can only succeed if they are approached in an integrated manner in which local authorities are fully involved. Labour absorption capacity of large industries is declining. This forces policy-making to be redirected to alternative sources of employment. The thesis contributes ways in which community-driven development programmes may be assessed at household and community levels. / Thesis (Ph.D. (Economics))--North-West University, Vaal Triangle Campus, 2004.

The thesis analyzes and compares tax burden on employees in the Czech Republic and Belgium. The first part summarizes the tax systems of the two countries, and describes how to proceed in the calculation of their tax burden. The second part deals with the comparison of effective tax rates for different types of taxpayers. The third part discusses the tax progressivity in terms of local progressivity, which is measured by using provided intervals and determines for which income categories is the progressivity most important. Lorenz curve in the last part shows graphically global tax progressivity and redistribution of income in society. The Gini coefficient measures it. Final evaluation highlights the important ties between the two countries, compares with other countries of the European Union and its future development especially in the area of taxation of wages.

The purpose of the master thesis is to compare the tax burden of employees in the Czech Republic and in the United States of America according to the legislation in 2016. The theoretical part is devoted to the description of tax systems, focusing on the taxation of income from employment. In the part United States I briefly mention the development of the tax system. The practical part consists of two chapters. The first one is focused on the calculation of the effective tax rate for taxpayers from selected types of households. The second one deals with global progressivity of the income tax. Equal income distribution in society is analyzed using the Lorenz curve and the Gini coefficient. The calculations indicate progressive tax effects both in the Czech Republic and in the United States with higher rate of tax progression and also higher inequality of income distribution in the United States. In the issue of effective rates of income tax is evident higher tax burden in the United States. Differences of total effective rates are decreasing between both countries.