The thesis is focused on the exploration of income inequality among citizens of the Czech Republic and Great Britain. It is a comparison that evaluates the state income redistribution through state social support benefits. It provides information, in which country exists greater income inequality in income distribution among households and whether the income inequality among the citizens decreased due to the payment of these benefits or not. The theoretical parts of the work are devoted to explanation of basic terms (such as income redistribution, instruments of redistribution, relationship between social policy and redistribution) and tools for measuring income inequality (Lorenz curve, Gini coefficient, Robin Hood index, Interquintile share ratio S80/S20). The text also describes the various state social support benefits of both countries. The main research section contains calculations and graphical representations of all the above mentioned indicators. The final values are compared and the results are summarized.

Chapter 1 introduces Jensen Inequality and its geometric interpretation. Some useful criteria for checking the convexity of functions are discussed. Many applications in various fields are also included. Chapter 2 deals with Schur Inequality, which can easily solve some problems involved symmetric inequality in three variables. The relationship between Schur Inequality and the roots and the coefficients of a cubic equation is also investigated. Chapter 3 presents Muirhead Inequality which is derived from the concept of majorization. It generalizes the inequality of arithmetic and geometric means. The equivalence of majorization and Muirhead¡¦s condition is illustrated. Two useful tricks for applying Muirhead Inequality are provided. Chapter 4 handles Majorization Inequality which involves Majorization and Schur convexity, two of the most productive concepts in the theory of inequalities. Its applications in elementary symmetric functions, sample variance, entropy and birthday problem are considered.

The purpose of this master thesis is comparing the taxation of income of employees in the Czech Republic and Germany. The theoretical part is focused on describing the taxation of income of employees in both analyzed states. This part also includes an explanation of the social insurance system in both countries. The empirical part of thesis oncentrates on a comparison between the tax burden of Czech and German employees among various income groups and various taxpayer. The tax burden is then compared with the effective tax rate. The final section of this thesis compares values of redistribution indicators, such as indicators of interval and global progressivity (Lorenz curve, Gini coefficient.

The purpose of this master thesis is comparison of the tax burden of Czech a Swedish employees. The first part describes tax systems of both analyzed states focusing on the taxation of income from employment according to the 2016 legislation in order to successfully perform the calculations in the following sections. The second, practical part is dedicated to the comparison of selected indicators. It consists of two parts. The first is focused on the calculation of average effective tax rate for various income groups and various types of taxpayers. The next part compares values of redistribution indicators, which are interval and global progressivity indicators (Lorenz curve, Gini coefficient). The final section is devoted to the comparison of conclusions of this thesis with conclusions of thesis with similar subject, that have been successfully defended.

The diploma thesis is focused on the distribution of non-taxable items, respectively their impact on the distribution of the income or tax base between diverse income groups in the Czech Republic. The aim of the empirical research was to measure redistributional effects of total and particular non-taxable items by various income inequality metrics.

The aim of this thesis is to compare effective income tax rate in Czech and Slovak republic. After introduction follows chapter which describes the tax systems in both countries with focus on personal income tax and social insurance. The third chapter defines indicators of effective labour taxation which are used for international comparison. Chapter four is comparing effective labour taxation in Czech and Slovak republic based on indicators defined in previous chapter. The fifth chapter is analysing inequality of income distribution and influence of income tax on redistribution. The progressivity of personal income tax in Czech and Slovak republic is measured by interval and global progressivity method. The conclusion is summarizing the outcomes of the thesis and suggests improvements for Czech tax system.

This master´s thesis compares a taxation of employment in the Czech Republic and in Austria. The effective tax rate and the effective rate of the total burden employee analyzes the tax burden on emplyee for various types of taxpayers. The next chapter examines the interval progressivity of taxes in both states and it evaluates, for which taxpayers a degree of progressivity of the income tax is the most sensitive. Lorenz curve before and after taxation in the last chapter shows the distribution of income between employees and the impact of taxation in order to redistribute the income in society. Coefficients compiled from the Lorenz curve for the Czech Republic and Austria quantify the degree of income redistribution through a progressive income tax.

The purpose of the thesis is to compare the taxation of the employee income in the Czech Republic and in Ireland with appropriate legislation of 2015. In theoretical part, I describe tax system of both states with an emphasis on taxation of income from employment. The theoretical part contains also a short summary of tax systems development. Practical part is divided into two different sections. First of them is focused on the calculation of effective tax rate for taxpayers in different types of households and the second one deals with the calculation of interval and global progressivity of tax in both countries, together with an analysis of income equality or inequality in society by using the Lorenz curve and the Gini coefficient. The calculations showed a progressive tax effects in both the Czech Republic and Ireland, with higher rate of tax progression and higher degree of income inequality in Ireland. From the perspective of effective income tax rates, higher tax burden is imposed in Ireland. The effective tax rate is on average 13.5 of percentage points higher than in the Czech Republic. This is also confirmed by the legal provision of the relevant tax legislation.

La répartition des revenus d'une population, la distribution des instants de défaillance d'un matériel et l'évolution des bénéfices des contrats d'assurance vie - étudiées en sciences économiques et de gestion – sont liées a des fonctions continues appartenant à la classe des fonctionnelles de la fonction de répartition. Notre thèse porte sur l'estimation à noyau de fonctionnelles de la fonction de répartition avec applications en sciences économiques et de gestion. Dans le premier chapitre, nous proposons des estimateurs polynomiaux locaux dans le cadre i.i.d. de deux fonctionnelles de la fonction de répartition, notées LF et TF , utiles pour produire des estimateurs lisses de la courbe de Lorenz et du temps total de test normalisé (scaled total time on test transform). La méthode d'estimation est décrite dans Abdous, Berlinet et Hengartner (2003) et nous prouvons le bon comportement asymptotique des estimateurs polynomiaux locaux. Jusqu'alors, Gastwirth (1972) et Barlow et Campo (1975) avaient défini des estimateurs continus par morceaux de la courbe de Lorenz et du temps total de test normalisé, ce qui ne respectait pas la propriété de continuité des courbes initiales. Des illustrations sur données simulées et réelles sont proposées. Le second chapitre a pour but de fournir des estimateurs polynomiaux locaux dans le cadre i.i.d. des dérivées successives des fonctionnelles de la fonction de répartition explorées dans le chapitre précédent. A part l'estimation de la dérivée première de la fonction TF qui se traite à l'aide de l'estimation lisse de la fonction de répartition, la méthode d'estimation employée est l'approximation polynomiale locale des fonctionnelles de la fonction de répartition détaillée dans Berlinet et Thomas-Agnan (2004). Divers types de convergence ainsi que la normalité asymptotique sont obtenus, y compris pour la densité et ses dérivées successives. Des simulations apparaissent et sont commentées. Le point de départ du troisième chapitre est l'estimateur de Parzen-Rosenblatt (Rosenblatt (1956), Parzen (1964)) de la densité. Nous améliorons dans un premier temps le biais de l'estimateur de Parzen-Rosenblatt et de ses dérivées successives à l'aide de noyaux d'ordre supérieur (Berlinet (1993)). Nous démontrons ensuite les nouvelles conditions de normalité asymptotique de ces estimateurs. Enfin, nous construisons une méthode de correction des effets de bord pour les estimateurs des dérivées de la densité, grâce aux dérivées d'ordre supérieur. Le dernier chapitre s'intéresse au taux de hasard, qui contrairement aux deux fonctionnelles de la fonction de répartition traitées dans le premier chapitre, n'est pas un rapport de deux fonctionnelles linéaires de la fonction de répartition. Dans le cadre i.i.d., les estimateurs à noyau du taux de hasard et de ses dérivées successives sont construits à partir des estimateurs à noyau de la densité et ses dérivées successives. La normalité asymptotique des premiers estimateurs est logiquement obtenue à partir de celle des seconds. Nous nous plaçons ensuite dans le modèle à intensité multiplicative, un cadre plus général englobant des données censurées et dépendantes. Nous menons la procédure à terme de Ramlau-Hansen (1983) afin d'obtenir les bonnes propriétés asymptotiques des estimateurs du taux de hasard et de ses dérivées successives puis nous tentons d'appliquer l'approximation polynomiale locale dans ce contexte. Le taux d'accumulation du surplus dans le domaine de la participation aux bénéfices pourra alors être estimé non parametriquement puisqu'il dépend des taux de transition (taux de hasard d'un état vers un autre) d'une chaine de Markov (Ramlau-Hansen (1991), Norberg (1999)) / The income distribution of a population, the distribution of failure times of a system and the evolution of the surplus in with-profit policies - studied in economics and management - are related to continuous functions belonging to the class of functionals of the distribution function. Our thesis covers the kernel estimation of some functionals of the distribution function with applications in economics and management. In the first chapter, we offer local polynomial estimators in the i.i.d. case of two functionals of the distribution function, written LF and TF , which are useful to produce the smooth estimators of the Lorenz curve and the scaled total time on test transform. The estimation method is described in Abdous, Berlinet and Hengartner (2003) and we prove the good asymptotic behavior of the local polynomial estimators. Until now, Gastwirth (1972) and Barlow and Campo (1975) have defined continuous piecewise estimators of the Lorenz curve and the scaled total time on test transform, which do not respect the continuity of the original curves. Illustrations on simulated and real data are given. The second chapter is intended to provide smooth estimators in the i.i.d. case of the derivatives of the two functionals of the distribution function presented in the last chapter. Apart from the estimation of the first derivative of the function TF with a smooth estimation of the distribution function, the estimation method is the local polynomial approximation of functionals of the distribution function detailed in Berlinet and Thomas-Agnan (2004). Various types of convergence and asymptotic normality are obtained, including the probability density function and its derivatives. Simulations appear and are discussed. The starting point of the third chapter is the Parzen-Rosenblatt estimator (Rosenblatt (1956), Parzen (1964)) of the probability density function. We first improve the bias of this estimator and its derivatives by using higher order kernels (Berlinet (1993)). Then we find the modified conditions for the asymptotic normality of these estimators. Finally, we build a method to remove boundary effects of the estimators of the probability density function and its derivatives, thanks to higher order derivatives. We are interested, in this final chapter, in the hazard rate function which, unlike the two functionals of the distribution function explored in the first chapter, is not a fraction of two linear functionals of the distribution function. In the i.i.d. case, kernel estimators of the hazard rate and its derivatives are produced from the kernel estimators of the probability density function and its derivatives. The asymptotic normality of the first estimators is logically obtained from the second ones. Then, we are placed in the multiplicative intensity model, a more general framework including censored and dependent data. We complete the described method in Ramlau-Hansen (1983) to obtain good asymptotic properties of the estimators of the hazard rate and its derivatives and we try to adopt the local polynomial approximation in this context. The surplus rate in with-profit policies will be nonparametrically estimated as its mathematical expression depends on transition rates (hazard rates from one state to another) in a Markov chain (Ramlau-Hansen (1991), Norberg (1999))