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Generalized Entropy Index
The generalized entropy index has been proposed as a measure of income inequality in a population. It is derived from information theory as a measure of redundancy in data. In information theory a measure of redundancy can be interpreted as non-randomness or data compression; thus this interpretation also applies to this index. In addition, interpretation of biodiversity as entropy has also been proposed leading to uses of generalized entropy to quantify biodiversity. Formula The formula for general entropy for real values of \alpha is: GE(\alpha) = \begin \frac\sum_^N\left left(\frac\right)^\alpha - 1\right& \alpha \ne 0, 1,\\ \frac\sum_^N\frac\ln\frac,& \alpha=1,\\ -\frac\sum_^N\ln\frac,& \alpha=0. \end where N is the number of cases (e.g., households or families), y_i is the income for case i and \alpha is a parameter which regulates the weight given to distances between incomes at different parts of the income distribution. For large \alpha the index is especially sensit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
South Africa Inequality (Generalized Entropy Measure, Parameter 2) (5457977862)
South is one of the cardinal directions or compass points. The direction is the opposite of north and is perpendicular to both west and east. Etymology The word ''south'' comes from Old English ''sūþ'', from earlier Proto-Germanic ''*sunþaz'' ("south"), possibly related to the same Proto-Indo-European root that the word ''sun'' derived from. Some languages describe south in the same way, from the fact that it is the direction of the sun at noon (in the Northern Hemisphere), like Latin meridies 'noon, south' (from medius 'middle' + dies 'day', ), while others describe south as the right-hand side of the rising sun, like Biblical Hebrew תֵּימָן teiman 'south' from יָמִין yamin 'right', Aramaic תַּימנַא taymna from יָמִין yamin 'right' and Syriac ܬܰܝܡܢܳܐ taymna from ܝܰܡܝܺܢܳܐ yamina (hence the name of Yemen, the land to the south/right of the Levant). South is sometimes abbreviated as S. Navigation By convention, the ''bottom or down-f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Income Inequality Metrics
Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of wealth, distribution of income and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general. While different theories may try to explain how income inequality comes about, income inequality descriptive statistic, metrics simply provide a Systems of measurement, system of measurement used to determine the dispersion of incomes. The concept of inequality is distinct from poverty and distributive justice, fairness. Income distribution has always been a central concern of economic theory and economic policy. Classical economists such as Adam Smith, Thomas Malthus and David Ricardo were mainly concerned with factor income distribution, that is, the distribution (economics), distribution of income between the main factors of production, land, labour and capital. It is often related to wealth distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rényi Entropy
In information theory, the Rényi entropy is a quantity that generalizes various notions of Entropy (information theory), entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is important in ecology and statistics as diversity indices, index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of Quantum entanglement, entanglement. In the Heisenberg XY spin chain model, the Rényi entropy as a function of can be calculated explicitly because it is an automorphic function with respect to a particular subgroup of the modular group. In theoretical computer science, the min-entropy is used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorenz Curve
In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing Economic inequality, inequality of the wealth distribution. The curve is a graph of a function, graph showing the proportion of overall income or wealth assumed by the bottom of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom of households, what percentage of the total income they have. The percentage of households is plotted on the -axis, the percentage of income on the -axis. It can also be used to show distribution of Asset (economics), assets. In such use, many economists consider it to be a measure of social inequality. The concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where the cumulative proportion of species is plotted a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Income Inequality Metrics
Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of wealth, distribution of income and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general. While different theories may try to explain how income inequality comes about, income inequality descriptive statistic, metrics simply provide a Systems of measurement, system of measurement used to determine the dispersion of incomes. The concept of inequality is distinct from poverty and distributive justice, fairness. Income distribution has always been a central concern of economic theory and economic policy. Classical economists such as Adam Smith, Thomas Malthus and David Ricardo were mainly concerned with factor income distribution, that is, the distribution (economics), distribution of income between the main factors of production, land, labour and capital. It is often related to wealth distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoover Index
The Hoover index, also known as the Robin Hood index or the Schutz index, is a measure of income inequality. It is equal to the percentage of the total population's income that would have to be redistribution of income and wealth, redistributed to make all the incomes equal. i.e. The Hoover is the total amount (as a percentage of the national-income) by which people have less than their equal income-share. The Hoover Index can be calculated by the following subtraction: The percentage of the people getting less than their equal-share (i.e. less than the national mean income), minus their percentage of the national income. It can be graphically represented as the longest vertical distance between the Lorenz curve (which graphs cumulative income vs cumulative population (income-ordered population-percentile)and the 45 degree line representing perfect equality). It would be informative to express the Hoover in terms of its average cost to individuals who get less than their equal- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gini Coefficient
In economics, the Gini coefficient ( ), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income distribution, income inequality, the wealth distribution, wealth inequality, or the consumption inequality within a nation or a social group. It was developed by Italian statistics, statistician and Sociology, sociologist Corrado Gini. The Gini coefficient measures the economic inequality, inequality among the values of a frequency distribution, such as income levels. A Gini coefficient of 0 reflects perfect equality, where all income or wealth values are the same. In contrast, a Gini coefficient of 1 (or 100%) reflects maximal inequality among values, where a single individual has all the income while all others have none. Corrado Gini proposed the Gini coefficient as a measure of social inequality, inequality of income inequality metrics, income or Wealth concentration, wealth. For Organisation for Economic Co-operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, in epidemiology, and in psychology/neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \sigma to the mean \mu, CV = \frac. It shows the extent of variability in relation to the mean of the population. The coefficien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theil Index
The Theil index is a statistic primarily used to measure economic inequality and other economic phenomena, though it has also been used to measure racial segregation. The Theil index ''T''T is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. It is a special case of the generalized entropy index. It can be viewed as a measure of redundancy, lack of diversity, isolation, segregation, inequality, non-randomness, and compressibility. It was proposed by a Dutch econometrician Henri Theil (1924–2000) at the Erasmus University Rotterdam. Henri Theil himself said (1967): "The (Theil) index can be interpreted as the expected information content of the indirect message which transforms the population shares as prior probabilities into the income shares as posterior probabilities." Amartya Sen noted, "But the fact remains that the Theil index is an arbitrary formula, and the average of the logarithms of the recip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Log Deviation
In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. The MLD is zero when everyone has the same income, and takes larger positive values as incomes become more unequal, especially at the high end. Definition The MLD of household income has been defined asJonathan Haughton and Shahidur R. Khandker. 2009. ''The Handbook on Poverty and Inequality''. Washington, DC: The World Bank. : \mathrm=\frac\sum_^N \ln \frac where N is the number of households, x_i is the income of household ''i'', and \overline is the mean of x_i. Naturally the same formula can be used for positive variables other than income and for units of observation other than households. Equivalent definitions are : \mathrm=\frac\sum_^N (\ln \overline - \ln x_i) =\ln \overline - \overline where \overline is the mean of ln(''x''). The last definition shows that MLD is nonnegative, since \ln \geq \overline by Jensen's inequality. MLD has been called "the standard devi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atkinson Index
The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution contributed most to the observed inequality. Definition The Atkinson index is defined as: :A_\varepsilon(y_1,\ldots,y_N)= \begin 1-\frac\left(\frac\sum_^y_^\right)^ & \mbox\ 0 \leq \varepsilon \neq 1 \\ 1-\frac\left(\prod_^y_\right)^ & \mbox\ \varepsilon=1 \\ 1-\frac\min \left(y_1,...,y_N\right) & \mbox\ \varepsilon=+\infty \end where y_ is individual income (''i'' = 1, 2, ..., ''N'') and \mu is the mean income. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean). Interpretation The index can be turned into a normative measure by imposing a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Income Inequality
In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long seen income and its distribution as a central concern. Unequal distribution of income causes economic inequality which is a concern in almost all countries around the world. About Classical economists such as Adam Smith (1723–1790), Thomas Malthus (1766–1834), and David Ricardo (1772–1823) concentrated their attention on factor income-distribution, that is, the distribution of income between the primary factors of production (land, labour and capital). Modern economists have also addressed issues of income distribution, but have focused more on the distribution of income across individuals and households. Important theoretical and policy concerns include the balance between income inequality and economic growth, and their often inverse relationship. The Lorenz curve can represent the distribution of income within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
