gini coefficient

Examples of gini coefficient in the following topics:

• Economic measures

  • The Gini coefficient (also known as the Gini index or Gini ratio) is a measure of statistical dispersion intended to represent the income distribution of a nation's residents.
  • The Gini coefficient measures the inequality among values of a frequency distribution.
  • A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income).
  • A Gini coefficient of one (or 100%) expresses maximal inequality among values (for example where only one person has all the income).
  • The Gini coefficient was originally proposed as a measure of inequality of income or wealth.

• Growing Gap Between Rich and Poor

  • There are various numerical indices for measuring economic inequality, but the most commonly used measure for the purposes of comparison is the Gini coefficient (also known as the Gini index or Gini ratio for Italian statistician and sociologist Corrado Gini).
  • The Gini coefficient is a statistical measure of the dispersal of wealth or income.
  • A Gini coefficient of zero indicates that there is perfect equality—assets are equally divided between all people in the group.
  • A Gini coefficient of one indicates that all of a group's wealth is held by one individual.
  • Using Gini coefficients, this map illustrates the extent to which each country in the world has internal inequality, or a gap between its richest and poorest citizens.

• Measuring Poverty

  • Relative poverty measures are used as official poverty rates in several developed countries and are measured according to several different income inequality metrics, including the Gini coefficient and the Theil Index.

• Distribution of Wealth and Income

  • The Gini coefficient measures the amount of wealth or income inequality in a society by plotting the proportion of total income (or wealth) earned by the bottom x percent of the population.

• Clustering

  • Figure 8.8 shows the output of Network>Cohesion>Clustering Coefficient as applied to the Knoke information network.
  • The "overall" graph clustering coefficient is simply the average of the densities of the neighborhoods of all of the actors.
  • Since larger graphs are generally (but not necessarily) less dense than smaller ones, the weighted average neighborhood density (or clustering coefficient) is usually less than the un-weighted version.
  • In assessing the degree of clustering, it is usually wise to compare the cluster coefficient to the overall density.

• Binary relations

  • Figure 13.7 shows the Jaccard coefficients for information receiving in the Knoke network, calculated using Tools>Similarities, and selecting "Jaccard."
  • Where data are sparse, and where there are very substantial differences in the degrees of points, the positive match coefficient is a good choice for binary or nominal data.
  • Figure 13.7 Jaccard coefficients for information receiving profiles in Knoke network

• Freeman's approach

  • One could examine whether the variability is high or low relative to the typical scores by calculating the coefficient of variation (standard deviation divided by mean, times 100) for in-degree and out-degree.
  • By the rules of thumb that are often used to evaluate coefficients of variation, the current values (35 for out-degree and 53 for in-degree) are moderate.

• Correlation between two networks with the same actors

  • Simple matching and the Jaccard coefficient are reasonable measures when both relations are binary; the Hamming distance is a measure of dissimilarity or distance between the scores in one matrix and the scores in the other (it is the number of values that differ, element-wise, from one matrix to the other).
  • To test the hypothesis that there is association, we look at the proportion of random trials that would generate a coefficient as large as (or as small as, depending on the measure) the statistic actually observed.

• Network regression

  • To estimate standard errors for R-squared and for the regression coefficients, we can use quadratic assignment.
  • We will run many trials with the rows and columns in the dependent matrix randomly shuffled, and recover the R-square and regression coefficients from these runs.

• Regressing position on attributes

  • Tools>Testing Hypotheses>Node-level>Regression will compute basic linear multiple regression statistics by OLS, and estimate standard errors and significance using the random permutations method for constructing sampling distributions of R-squared and slope coefficients.
  • As before, the coefficients are generated by standard OLS linear modeling techniques, and are based on comparing scores on independent and dependent attributes of individual actors.