BACKGROUND: Differences in disease-modifying therapy (DMT) prescribing patterns between different groups of neurologists have not been explored. HYPOTHESIS: MS-specialist neurologists use a broader range of DMTs in contrast to generalist neurologists who preferentially prescribe Avonex. METHODS: Ontario neurologist demographic and geographical characteristics were linked to 2009 DMT prescription data. Lorenz curves and Gini coefficients were constructed to examine prescribing patterns; separating neurologist characteristics dichotomously and separating Avonex from the other DMTs. Gini Coefficients were compared using jack-knife statistical techniques to derive 95% confidence intervals. RESULTS: Prescriptions are highly concentrated with 12% of Ontario neurologists prescribing 80% of DMTs. High-volume prescribers show a broader range of DMT use while low-volume prescribers tend to use a particular DMT. CONCLUSIONS: The majority of DMTs are prescribed by a small subset of neurologists. High-volume prescribers show more variability in DMT use while low-volume prescribers tend to individually focus on a narrower range of DMTs.

BACKGROUND: Differences in disease-modifying therapy (DMT) prescribing patterns between different groups of neurologists have not been explored. HYPOTHESIS: MS-specialist neurologists use a broader range of DMTs in contrast to generalist neurologists who preferentially prescribe Avonex. METHODS: Ontario neurologist demographic and geographical characteristics were linked to 2009 DMT prescription data. Lorenz curves and Gini coefficients were constructed to examine prescribing patterns; separating neurologist characteristics dichotomously and separating Avonex from the other DMTs. Gini Coefficients were compared using jack-knife statistical techniques to derive 95% confidence intervals. RESULTS: Prescriptions are highly concentrated with 12% of Ontario neurologists prescribing 80% of DMTs. High-volume prescribers show a broader range of DMT use while low-volume prescribers tend to use a particular DMT. CONCLUSIONS: The majority of DMTs are prescribed by a small subset of neurologists. High-volume prescribers show more variability in DMT use while low-volume prescribers tend to individually focus on a narrower range of DMTs.

Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples on income are used to evaluate the applicability of these methods: the first example is the 2001 income data from the Panel Study of Income Dynamics (PSID) and the second example makes use of households’ median income for the USA by counties for the years 1999 and 2006

The thesis presents results from five related studies concerned with the development and application of analytical techniques for the measurement of inequality. Four of the research pieces are analytical works focusing on the methodology of inequality measurement, while the fifth is an empirical study of income mobility and inequality in Australia. The most significant work of the dissertation is concerned with the derivation of a new information-theoretic index for the measurement of inequality. The proposed index is based upon the same relationship between information theory and inequality measurement used for the construction of Generalized Entropy (GE) inequality measures and is equivalent to a technique established in the field of signal processing. The measure shares the axiomatic superiority of GE measures over other measurement techniques and exhibits an additional attractive decomposition property such that the contribution of any set of individuals towards inequality is directly observable. No existing axiomatically complete measure possesses this property and thus the new measure has a degree of dominance over other techniques such as the Gini coefficient and Theil’s entropy measures. An empirical illustration of the new index using U.S. unit record income data is provided to demonstrate the alternative decomposition technique. It is shown that persons self-described as ‘White’ or ‘Japanese’ in the U.S. census drive a greater proportion of total inequality than persons from other racial groups relative to their respective population sizes. Other theoretical work in the thesis focuses on the construction and interpretation of Lorenz curves. A new parametric functional form for estimating the Lorenz curve is presented and closed form expressions for the implicit probability density function, cumulative distribution function and Gini coefficient are derived. Furthermore the proposed Lorenz curve is shown to provide a better fit to a range of real world data than other single parameter specifications such as the Pareto formulation. In a separate chapter the issue of Lorenz curve determination is addressed by determining a convex spline to interpolate Lorenz curves from grouped data. The spline is shown to provide better estimates of the Gini coefficient than other interpolation techniques and always satisfies the regularity conditions required for a Lorenz curve. Additional work on Lorenz curves examines the link between these functions and GE inequality metrics. In the thesis it is shown that these indices may be derived as direct functions of the Lorenz curve and analytical expressions for various GE measures are given in terms of Lorenz curve parameters. These results provide a basis for studying the effect of Lorenz curve construction upon the calculation of entropy based inequality measurements. The thesis concludes with an empirical study into income inequality and mobility in Australia using the HILDA unit record and household data panel. The research shows that Australian income mobility is slightly lower than in other developed countries and that much of the observed mobility occurs at the lower end of the income distribution.

The thesis presents results from five related studies concerned with the development and application of analytical techniques for the measurement of inequality. Four of the research pieces are analytical works focusing on the methodology of inequality measurement, while the fifth is an empirical study of income mobility and inequality in Australia. The most significant work of the dissertation is concerned with the derivation of a new information-theoretic index for the measurement of inequality. The proposed index is based upon the same relationship between information theory and inequality measurement used for the construction of Generalized Entropy (GE) inequality measures and is equivalent to a technique established in the field of signal processing. The measure shares the axiomatic superiority of GE measures over other measurement techniques and exhibits an additional attractive decomposition property such that the contribution of any set of individuals towards inequality is directly observable. No existing axiomatically complete measure possesses this property and thus the new measure has a degree of dominance over other techniques such as the Gini coefficient and Theil’s entropy measures. An empirical illustration of the new index using U.S. unit record income data is provided to demonstrate the alternative decomposition technique. It is shown that persons self-described as ‘White’ or ‘Japanese’ in the U.S. census drive a greater proportion of total inequality than persons from other racial groups relative to their respective population sizes. Other theoretical work in the thesis focuses on the construction and interpretation of Lorenz curves. A new parametric functional form for estimating the Lorenz curve is presented and closed form expressions for the implicit probability density function, cumulative distribution function and Gini coefficient are derived. Furthermore the proposed Lorenz curve is shown to provide a better fit to a range of real world data than other single parameter specifications such as the Pareto formulation. In a separate chapter the issue of Lorenz curve determination is addressed by determining a convex spline to interpolate Lorenz curves from grouped data. The spline is shown to provide better estimates of the Gini coefficient than other interpolation techniques and always satisfies the regularity conditions required for a Lorenz curve. Additional work on Lorenz curves examines the link between these functions and GE inequality metrics. In the thesis it is shown that these indices may be derived as direct functions of the Lorenz curve and analytical expressions for various GE measures are given in terms of Lorenz curve parameters. These results provide a basis for studying the effect of Lorenz curve construction upon the calculation of entropy based inequality measurements. The thesis concludes with an empirical study into income inequality and mobility in Australia using the HILDA unit record and household data panel. The research shows that Australian income mobility is slightly lower than in other developed countries and that much of the observed mobility occurs at the lower end of the income distribution.

Low income proportion (LIP), Lorenz curve (LC) and generalized Lorenz curve (GLC) are important indexes in describing the inequality of income distribution. They have been widely used for measuring social stability by governments around the world. The accuracy of estimating those indexes is essential to quantify the economics of a country. Established statistical inferential methods for these indexes are based on an asymptotic normal distribution, which may have poor performance when the real income data is skewed or has outliers. Recent applications of nonparametric methods, though, allow researchers to utilize techniques without giving data the parametric distribution assumption. For example, existing research proposes the plug-in empirical likelihood (EL)-based inferences for LIP, LC and GLC. However, this method becomes computationally intensive and mathematically complex because of the presence of nonlinear constraints in the underlying optimization problem. Meanwhile, the limiting distribution of the log empirical likelihood ratio is a scaled Chi-square distribution. The estimation of the scale constant will affect the overall performance of the plug-in EL method. To improve the efficiency of the existing inferential methods, this dissertation first proposes kernel estimators for LIP, LC and GLC, respectively. Then the cross-validation method is proposed to choose bandwidth for the kernel estimators. These kernel estimators are proved to have asymptotic normality. The smoothed jackknife empirical likelihood (SJEL) for LIP, LC and GLC are defined. Then the log-jackknife empirical likelihood ratio statistics are proved to follow the standard Chi-square distribution. Extensive simulation studies are conducted to evaluate the kernel estimators in terms of Mean Square Error and Asymptotic Relative Efficiency. Next, the SJEL-based confidence intervals and the smoothed bootstrap-based confidence intervals are proposed. The coverage probability and interval length for the proposed confidence intervals are calculated and compared with the normal approximation-based intervals. The proposed kernel estimators are found to be competitive estimators, and the proposed inferential methods are observed to have better finite-sample performance. All inferential methods are illustrated through real examples.

This thesis is focused on questions of state redistribution and income inequality in the Czech republic. It explains the main ideas of state redistribution, income inequality and relation between them. It anlyzes the particular instruments of state redistribution such as tax systems and systems of social transfers which the government uses to achiave more equal distribution of incomes in society. The object of the thesis is to find out how the particular instruments contribute to filling the essentials goal - lower the income inequality in society. It is based on the data from years 2006 until 2008 from the statistics of household accounts published on the web site of the Czech statistical office. Finally, it is devoted to the trends of state redistribution and income inequality in OECD countries.

The purpose of this paper is to investigate the correlation between income inequality and economic growth in a cross-section of 90 countries from 2002 to 2006. The controversial Kuznets Hypothesis, the economic model that hypothesizes the relationship between inequality and per capita income is an inverted U-shaped curve, is scrutinized and investigated to consider its viability and accuracy. A multiple linear regression model is estimated and the viability of the regression model is supported by several statistical tests. Based on the estimated model, a negative correlation between growth and inequality has been found.

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This diploma thesis deals with the problematics of redistribution of public finance. The factors interfering in the process of redistribution are described here. The attention is paid to equality of redistribution of incomes within the group of monitored households. Since the level of redistribution is influenced by different factors, their analyses are carried out here. The levels of incomes redistribution inequality here are measured in monitored Czech hoseholds in the years 2005 until 2007. Calculations comprise analyses of individual types of incomes and items which influence equality of redistribution. A part of conclusion consists of comparison of the results from the mentioned statistics with the data published by OECD. The main aim of the thesis is confirmation or negation of the following hypothesis: "Tax system and social security system markedly influences redistribution of incomes in Czech households.".