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Luxembourg **Inequality Stats**

#### Definitions

- GINI index: Gini index measures the extent to which the distribution of income (or, in some cases, consumption expenditure) among individuals or households within an economy deviates from a perfectly equal distribution. A Lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. The Gini index measures the area between the Lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line. Thus a Gini index of 0 represents perfect equality, while an index of 100 implies perfect inequality."
- Gini coefficient > Level: Income is defined as household disposable income in a particular year. It consists of earnings, self-employment and capital income and public cash transfers; income taxes and social security contributions paid by households are deducted. The income of the household is attributed to each of its members, with an adjustment to reflect differences in needs for households of different sizes (i.e. the needs of a household composed of four people are assumed to be twice as large as those of a person living alone).Income inequality among individuals is measured here by five indicators. The Gini Coefficient is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive, and it ranges between 0 in the case of perfect equality and 1 in the case of perfect inequality. The mean log deviation is the average value of the logarithm of the ratio of mean income to the income of each decile. The squared coefficient of variation is the variance of average income of each decile, divided by the square of the average income of the entire population. The P90/P10 ratio is the ratio of the upper bound value of the ninth decile (i.e. the 10% of people with highest income) to that of the first. The P50/P10 ratio is the ratio of median income to the upper bound value of the first decile. The mean log deviation and inter-decile ratios have a lower value of 1 and no upper bound, while the squared coefficient of variation has a lower bound of 0 and upper bound of infinity.
- Income share held by fourth 20%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles. Percentage shares by quintile may not sum to 100 because of rounding.
- Income share held by highest 10%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles.
- Income share held by highest 20%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles. Percentage shares by quintile may not sum to 100 because of rounding.
- Income share held by lowest 10%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles.
- Income share held by lowest 20%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles. Percentage shares by quintile may not sum to 100 because of rounding.
- Income share held by second 20%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles. Percentage shares by quintile may not sum to 100 because of rounding.
- Income share held by third 20%: Percentage share of income or consumption is the share that accrues to subgroups of population indicated by deciles or quintiles. Percentage shares by quintile may not sum to 100 because of rounding.
- Interdecile ratio P50/P10 > Level: Income is defined as household disposable income in a particular year. It consists of earnings, self-employment and capital income and public cash transfers; income taxes and social security contributions paid by households are deducted. The income of the household is attributed to each of its members, with an adjustment to reflect differences in needs for households of different sizes (i.e. the needs of a household composed of four people are assumed to be twice as large as those of a person living alone).Income inequality among individuals is measured here by five indicators. The Gini Coefficient is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive, and it ranges between 0 in the case of perfect equality and 1 in the case of perfect inequality. The mean log deviation is the average value of the logarithm of the ratio of mean income to the income of each decile. The squared coefficient of variation is the variance of average income of each decile, divided by the square of the average income of the entire population. The P90/P10 ratio is the ratio of the upper bound value of the ninth decile (i.e. the 10% of people with highest income) to that of the first. The P50/P10 ratio is the ratio of median income to the upper bound value of the first decile. The mean log deviation and inter-decile ratios have a lower value of 1 and no upper bound, while the squared coefficient of variation has a lower bound of 0 and upper bound of infinity.
- Interdecile ratio P50/P10 > Rank: Income is defined as household disposable income in a particular year. It consists of earnings, self-employment and capital income and public cash transfers; income taxes and social security contributions paid by households are deducted. The income of the household is attributed to each of its members, with an adjustment to reflect differences in needs for households of different sizes (i.e. the needs of a household composed of four people are assumed to be twice as large as those of a person living alone).Income inequality among individuals is measured here by five indicators. The Gini Coefficient is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive, and it ranges between 0 in the case of perfect equality and 1 in the case of perfect inequality. The mean log deviation is the average value of the logarithm of the ratio of mean income to the income of each decile. The squared coefficient of variation is the variance of average income of each decile, divided by the square of the average income of the entire population. The P90/P10 ratio is the ratio of the upper bound value of the ninth decile (i.e. the 10% of people with highest income) to that of the first. The P50/P10 ratio is the ratio of median income to the upper bound value of the first decile. The mean log deviation and inter-decile ratios have a lower value of 1 and no upper bound, while the squared coefficient of variation has a lower bound of 0 and upper bound of infinity.
- Interdecile ratio P90/P10 > Rank: Income is defined as household disposable income in a particular year. It consists of earnings, self-employment and capital income and public cash transfers; income taxes and social security contributions paid by households are deducted. The income of the household is attributed to each of its members, with an adjustment to reflect differences in needs for households of different sizes (i.e. the needs of a household composed of four people are assumed to be twice as large as those of a person living alone).Income inequality among individuals is measured here by five indicators. The Gini Coefficient is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive, and it ranges between 0 in the case of perfect equality and 1 in the case of perfect inequality. The mean log deviation is the average value of the logarithm of the ratio of mean income to the income of each decile. The squared coefficient of variation is the variance of average income of each decile, divided by the square of the average income of the entire population. The P90/P10 ratio is the ratio of the upper bound value of the ninth decile (i.e. the 10% of people with highest income) to that of the first. The P50/P10 ratio is the ratio of median income to the upper bound value of the first decile. The mean log deviation and inter-decile ratios have a lower value of 1 and no upper bound, while the squared coefficient of variation has a lower bound of 0 and upper bound of infinity.
- Mean log deviation > Rank: Income is defined as household disposable income in a particular year. It consists of earnings, self-employment and capital income and public cash transfers; income taxes and social security contributions paid by households are deducted. The income of the household is attributed to each of its members, with an adjustment to reflect differences in needs for households of different sizes (i.e. the needs of a household composed of four people are assumed to be twice as large as those of a person living alone).Income inequality among individuals is measured here by five indicators. The Gini Coefficient is based on the comparison of cumulative proportions of the population against cumulative proportions of income they receive, and it ranges between 0 in the case of perfect equality and 1 in the case of perfect inequality. The mean log deviation is the average value of the logarithm of the ratio of mean income to the income of each decile. The squared coefficient of variation is the variance of average income of each decile, divided by the square of the average income of the entire population. The P90/P10 ratio is the ratio of the upper bound value of the ninth decile (i.e. the 10% of people with highest income) to that of the first. The P50/P10 ratio is the ratio of median income to the upper bound value of the first decile. The mean log deviation and inter-decile ratios have a lower value of 1 and no upper bound, while the squared coefficient of variation has a lower bound of 0 and upper bound of infinity.

SOURCES: World Bank, Development Research Group. Data are based on primary household survey data obtained from government statistical agencies and World Bank country departments. Data for high-income economies are from the Luxembourg Income Study database. For more information and methodology, please see PovcalNet (http://iresearch.worldbank.org/PovcalNet/jsp/index.jsp).; OECD Country statistical profiles 2009