For example, Sastre and Ayala

For example, Sastre and Ayala, conclude from their study of income Gini coefficient data between 1993 and 1998 for six developed economies, that France had the least income mobility, Italy the highest, and the United States and Germany intermediate levels of income mobility over those 5 years. HP Pavilion dv7-2250sf CPU Fan Gini coefficient has features that make it useful as a measure of dispersion in a population, and inequalities in particular.^[45] It is a ratio analysis method making it easier to interpret. It also avoids references to a statistical average or position unrepresentative of most of the population, such as per capita income or gross domestic product. HP 434678-001 CPU Fan For a given time interval, Gini coefficient can therefore be used to compare diverse countries and different regions or groups within a country; for example states, counties, urban versus rural areas, gender and ethnic groups. Gini coefficients can be used to compare income distribution over time, thus it is possible to see if inequality is increasing or decreasing independent of absolute incomes. HP G60-230us CPU Fan The Gini coefficient is a relative measure. Its proper use and interpretation is controversial.^[49] Mellor explains^[50] it is possible for the Gini coefficient of a developing country to rise (due to increasing inequality of income) while the number of people in absolute poverty decreases. This is because the Gini coefficient measures relative, HP Pavilion dv6365us CPU Fan not absolute, wealth. Kwok concludes^[51] that changing income inequality, measured by Gini coefficients, can be due to structural changes in a society such as growing population (baby booms, aging populations, increased divorce rates, extended family households splitting into nuclear families, emigration, immigration) and income mobility. HP 535439-001 CPU Fan Gini coefficients are simple, and this simplicity can lead to oversights and can confuse the comparison of different populations; for example, while both Bangladesh (per capita income of $1,693) and the Netherlands (per capita income of $42,183) had an income Gini index of 0.31 in 2010,^[52] COMPAQ 6910c CPU Fan the quality of life, economic opportunity and absolute income in these countries are very different, i.e. countries may have identical Gini coefficients, but differ greatly in wealth. Basic necessities may be available to all in a developed economy, while in an undeveloped economy with the same Gini coefficient, basic necessities may be unavailable to most or unequally available, due to lower absolute wealth. IBM Lenovo IdeaPad G510 CPU Fan Even when the total income of a population is the same, in certain situations two countries with different income distributions can have the same Gini index (e.g. cases when income Lorenz Curves cross).^[45] Table A illustrates one such situation. Both countries have a Gini index of 0.2, but the average income distributions for household groups are different. HP G62-110SO CPU Fan As another example, in a population where the lowest 50% of individuals have no income and the other 50% have equal income, the Gini coefficient is 0.5; whereas for another population where the lowest 75% of people have 25% of income and the top 25% have 75% of the income, the Gini index is also 0.5. DELL Precision M6400 CPU Fan Economies with similar incomes and Gini coefficients can have very different income distributions. Bellù and Liberati claim that to rank income inequality between two different populations based on their Gini indices is sometimes not possible, or misleading. A Gini index does not contain information about absolute national or personal incomes. SONY Vaio VPC-EB290X CPU Fan Populations can have very low income Gini indices, yet simultaneously very high wealth Gini index. By measuring inequality in income, the Gini ignores the differential efficiency of use of household income. By ignoring wealth (except as it contributes to income) the Gini can create the appearance of inequality when the people compared are at different stages in their life. HP Envy 17-1090eo CPU Fan Wealthy countries such as Sweden can show a low Gini coefficient for disposable income of 0.31 thereby appearing equal, yet have very high Gini coefficient for wealth of 0.79 to 0.86 thereby suggesting an extremely unequal wealth distribution in its society.^[54][55] These factors are not assessed in income-based Gini. Toshiba Satellite A210-1CF CPU Fan Gini index has a downward-bias for small populations.^[56] Counties or states or countries with small populations and less diverse economies will tend to report small Gini coefficients. For economically diverse large population groups, a much higher coefficient is expected than for each of its regions. Taking world economy as one, and income distribution for all human beings, Dell Vostro 3450 CPU Fan for example, different scholars estimate global Gini index to range between 0.61 and 0.68.^[9][10] As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) for the same distribution. Toshiba Satellite A10-103 CPU Fan Philippe Monfort has shown that using inconsistent or unspecified granularity limits the usefulness of Gini coefficient measurements.^[57] The Gini coefficient measure gives different results when applied to individuals instead of households, for the same economy and same income distributions. Compaq Presario A900 CTO CPU Fan If household data is used, the measured value of income Gini depends on how the household is defined. When different populations are not measured with consistent definitions, comparison is not meaningful. Deininger and Squire (1996) show that income Gini coefficient based on individual income, rather than household income, are different. ACER Aspire 4736ZG CPU Fan For United States, for example, they find that individual income-based Gini index was 0.35, while for France they report individual income-based Gini index to be 0.43. According to their individual focussed method, in the 108 countries they studied, South Africa had the world's highest Gini index at 0.62, Toshiba Satellite A10-103 CPU Fan Malaysia had Asia's highest Gini index at 0.5, Brazil the highest at 0.57 in Latin America and Caribbean region, and Turkey the highest at 0.5 in OECD countries. Expanding on the importance of life-span measures, the Gini coefficient as a point-estimate of equality at a certain time, ignores life-span changes in income. SONY MCF-519PAM05 CPU Fan Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality, simply because people generally have lower incomes and wealth when they are young than when they are old. Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of inequality when none exist taking into account demographic effects. SONY Vaio VPC-EB290X CPU Fan Thus a given economy may have a higher Gini coefficient at any one point in time compared to another, while the Gini coefficient calculated over individuals' lifetime income is actually lower than the apparently more equal (at a given point in time) economy's.^[13] Essentially, what matters is not just inequality in any particular year, but the composition of the distribution over time. HP Pavilion dv7-2043cl CPU Fan Kwok claims income Gini index for Hong Kong has been high (0.434 in 2010^[52]), in part because of structural changes in its population. Over recent decades, Hong Kong has witnessed increasing numbers of small households, elderly households and elderly living alone. The combined income is now split into more households. HP Pavilion dv7-2130ev CPU Fan Many old people are living separately from their children in Hong Kong. These social changes have caused substantial changes in household income distribution. Income Gini coefficient, claims Kwok, does not discern these structural changes in its society.^[51] Household money income distribution for the United States, HP 608772-001 CPU Fan summarized in Table C of this section, confirms that this issue is not limited to just Hong Kong. According to the US Census Bureau, between 1979 and 2010, the population of United States experienced structural changes in overall households, the income for all income brackets increased in inflation-adjusted terms, household income distributions shifted into higher income brackets over time, while the income Gini coefficient increased.^[59][60] Toshiba Satellite A100-194 CPU Fan Another limitation of Gini coefficient is that it is not a proper measure of egalitarianism, as it is only measures income dispersion. For example, if two equally egalitarian countries pursue different immigration policies, the country accepting a higher proportion of low-income or impoverished migrants will report a higher Gini coefficient and therefore may appear to exhibit more income inequality. HP Pavilion tx1205/ CT CPU Fan Arnold describes one limitation of Gini coefficient to be income distribution situations where it misleads. The income of poorest fifth of households can be lower when Gini coefficient is lower, than when the poorest income bracket is earning a larger percentage of all income. Table D illustrates this case, HP Pavilion dv6640ep CPU Fan where the lowest income bracket has an average household market income of $500 per year at Gini index of 0.51, and zero income at Gini index of 0.48. This is counter-intuitive and Gini coefficient cannot tell what is happening to each income bracket or the absolute income, cautions Arnold.^[61][62] COMPAQ Presario CQ42-401TU CPU Fan Feldstein similarly explains one limitation of Gini coefficient as its focus on relative income distribution, rather than real levels of poverty and prosperity in society.^[63] He claims Gini coefficient analysis is limited because in many situations it intuitively implies inequality that violate the so-called Pareto improvement principle. Toshiba Satellite A300D CPU Fan The Pareto improvement principle, named after the Italian economist Vilfredo Pareto, states that a social, economic or income change is good if it makes one or more people better off without making anyone else worse off. Gini coefficient can rise if some or all income brackets experience a rising income. Feldstein’s explanation is summarized in Table D. HP Pavilion dv8397ea CPU  Fan The table shows that in a growing economy, consistent with Pareto improvement principle, where income of every segment of the population has increased, from one year to next, the income inequality Gini coefficient can rise too. In contrast, in another economy, if everyone gets poorer and is worse off, income inequality is less and Gini coefficient lower. HP Pavilion dv9821ea CPU Fan Some countries distribute benefits that are difficult to value. Countries that provide subsidized housing, medical care, education or other such services are difficult to value objectively, as it depends on quality and extent of the benefit. In absence of free markets, valuing these income transfers as household income is subjective. HP COMPAQ TC4200 CPU Fan The theoretical model of Gini coefficient is limited to accepting correct or incorrect subjective assumptions.In subsistence-driven and informal economies, people may have significant income in other forms than money, for example through subsistence farming orbartering. These income tend to accrue to the segment of population that is below-poverty line or very poor, SONY Vaio VGN-NW228F CPU Fan in emerging and transitional economy countries such as those in sub-Saharan Africa, Latin America, Asia and Eastern Europe. Informal economy accounts for over half of global employment and as much as 90 per cent of employment in some of the poorer sub-Saharan countries with high official Gini inequality coefficients. HP G62-b16ST CPU Fan Schneider et al., in their 2010 study of 162 countries,^[66] report about 31.2%, or about $20 trillion, of world's GDP is informal. In developing countries, the informal economy predominates for all income brackets except for the richer, urban upper income bracket populations. Even in developed economies, between 8% (United States) to 27% (Italy) of each nation's GDP is informal, HP 580696-001 CPU Fan and resulting informal income predominates as a livelihood activity for those in the lowest income brackets.^[67] The value and distribution of the incomes from informal or underground economy is difficult to quantify, making true income Gini coefficients estimates difficult.^[63][64] Different assumptions and quantifications of these incomes will yield different Gini coefficients.^[ HP Pavilion dv6-3049tx CPU Fan Gini has some mathematical limitations as well. It is not additive and different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets.Given the limitations of Gini coefficient, other statistical methods are used in combination or as an alternative measure of population dispersity. For example,entropy measures are frequently used (e.g. the Theil Index and the Atkinson index). HP G42-380LA CPU Fan These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution, which would occur if these agents acted like non-intelligent particles in a closed system following the laws of statistical physics. Although the Gini coefficient is most popular in economics, it can in theory be applied in any field of science that studies a distribution. Toshiba Qosmio G30-167 CPU Fan For example, in ecology the Gini coefficient has been used as a measure of biodiversity, where the cumulative proportion of species is plotted against cumulative proportion of individuals.^[75] In health, it has been used as a measure of the inequality of health related quality of life in a population.^[76] In education, it has been used as a measure of the inequality of universities.^[77] HP Pavilion dv7-1157cl CPU Fan In chemistry it has been used to express the selectivity of protein kinase inhibitors against a panel of kinases.^[78] In engineering, it has been used to evaluate the fairness achieved by Internet routers in scheduling packet transmissions from different flows of traffic.^[79] In statistics, building decision trees, it is used to measure the purity of possible child nodes, Compaq Presario CQ40-408AX CPU Fan with the aim of maximising the average purity of two child nodes when splitting, and it has been compared with other equality measures.^[80] The Gini coefficient is sometimes used for the measurement of the discriminatory power of rating systems in credit risk management.^[81] HP Mini 110-1110ET CPU Fan The discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients. The formula  , in calculation section above, may be used for the final model and also at individual model factor level, to quantify the discriminatory power of individual factors. It is related to accuracy ratio in population assessment models. HP Pavilion dv7-1157cl CPU Fan A diversity index is a quantitative measure that reflects how many different types (such as species) there are in a dataset, and simultaneously takes into account how evenly the basic entities (such as individuals) are distributed among those types. The value of a diversity index increases both when the number of types increases and when evenness increases. HP Pavilion dv6-3163eo CPU Fan For a given number of types, the value of a diversity index is maximized when all types are equally abundant.When diversity indices are used in ecology, the types of interest are usually species, but they can also be other categories, such as genera, families,functional types or haplotypes. The entities of interest are usually individual plants or animals, HP Pavilion dv9740us CPU Fan and the measure of abundance can be, for example, number of individuals, biomass or coverage. In demography, the entities of interest can be people, and the types of interest various demographic groups. In information science, the entities can be characters and the types the different letters of the alphabet. HP COMPAQ NX9420 CPU Fan The most commonly used diversity indices are simple transformations of the effective number of types (also known as 'true diversity'), but each diversity index can also be interpreted in its own right as a measure corresponding to some real phenomenon (but a different one for each diversity index). HP Pavilion dv7-4150ec CPU Fan True diversity, or the effective number of types, refers to the number of equally-abundant types needed for the average proportional abundance of the types to equal that observed in the dataset of interest (where all types may not be equally abundant). The true diversity in a dataset is calculated by first taking the weighted generalized mean of the proportional abundances of the types in the dataset, and then taking the inverse of this. HP Pavilion dv5-1102tu CPU Fan The denominator equals average proportional abundance of the types in the dataset as calculated with the weighted generalized mean with exponent q - 1. In the equation, R is richness (the total number of types in the dataset), and the proportional abundance of the ith type is . The proportional abundances themselves are used as the nominal weights. SONY VGN-SZ220 CPU Fan he value of q is often referred to as the order of the diversity. It defines the sensitivity of the diversity value to rare vs. abundant species by modifying how the mean of the species proportional abundances is calculated. With some values of the parameter q, the generalized mean with exponent q - 1 gives familiar kinds of mean as special cases. HP Pavilion dv7-6011tx CPU Fan In particular, q = 0 corresponds to the harmonic mean, q = 1 to the geometric mean and q = 2 to the arithmetic mean. As qapproaches infinity, the generalized mean with exponent q - 1 approaches the maximum   value, which is the proportional abundance of the most abundant species in the dataset. HP Pavilion dv5-1040eb CPU Fan In practice, increasing the value of q hence increases the effective weight given to the most abundant species. This leads to obtaining a larger mean   value and a smaller true diversity (^qD) value.When q = 1, the geometric mean of the   values is used, and each species is exactly weighted by its proportional abundance (in the geometric mean, weights are the exponents). ASUS F3Jv CPU Fan When q > 1, the weight given to abundant species is exaggerated, and when q < 1, the weight given to rare species is. At q = 0, the species weights exactly cancel out the species proportional abundances, such that mean   equals 1/R even when all species are not equally abundant. At q = 0, the effective number of species (⁰D) hence equals the actual number of species (R). IBM ThinkPad R50p 2887 CPU Fan In the context of diversity, q is generally limited to non-negative values. This is because negative values of q would give rare species so much more weight than abundant ones that ^qD would exceed R. Richness R simply quantifies how many different types the dataset of interest contains. SONY VGN-CS36GJ/R CPU Fan For example, species richness (usually notated S) of a dataset is the number of different species in the corresponding species list. Richness is a simple measure, so it has been a popular diversity index in ecology, where abundance data are often not available for the datasets of interest. Toshiba Satellite A215-S4807 CPU Fan Because richness does not take the abundances of the types into account, it is not the same thing as diversity, which does take abundances into account. However, if true diversity is calculated with q = 0, the effective number of types (⁰D) equals the actual number of types (R). The Shannon index has been a popular diversity index in the ecological literature, Toshiba Satellite Pro M10-SP405 CPU Fan where it is also known as Shannon's diversity index, the Shannon-Wiener index, the Shannon-Weaver index and the Shannon entropy. The measure was originally proposed by Claude Shannon to quantify the entropy (uncertainty or information content) in strings of text.^[5] The idea is that the more different letters there are, HP Pavilion dv4-1120us CPU Fan and the more equal their proportional abundances in the string of interest, the more difficult it is to correctly predict which letter will be the next one in the string. The Shannon entropy quantifies the uncertainty (entropy or degree of surprise) associated with this prediction. In ecology,   is often the proportion of individuals belonging to the ith species in the dataset of interest. Compaq Presario C550EM CPU Fan Then the Shannon entropy quantifies the uncertainty in predicting the species identity of an individual that is taken at random from the dataset. Although the equation is here written with natural logarithms, the base of the logarithm used when calculating the Shannon entropy can be chosen freely. Toshiba Qosmio E15-AV101 CPU Fan Shannon himself discussed logarithm bases 2, 10 and e, and these have since become the most popular bases in applications that use the Shannon entropy. Each log base corresponds to a different measurement unit, which have been called binary digits (bits), decimal digits (decits) and natural digits (nats) for the bases 2, 10 and e, respectively. Toshiba Satellite L645D-S4056 CPU Fan Comparing Shannon entropy values that were originally calculated with different log bases requires converting them to the same log base: change from the base a to base b is obtained with multiplication by log_ba. Toshiba Satellite A305-S6837 CPU Fan,HP Pavilion dv7-4087cl CPU Fan,HP Pavilion dv5-1118es CPU Fan