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Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
Income inequality metrics or income distribution metrics are used by social scientists to measure the 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.
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and 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).
Economic inequality is an umbrella term for a) income inequality or distribution of income (how the total sum of money paid to people is distributed among them), b) wealth inequality or distribution of wealth (how the total sum of wealth owned by people is distributed among the owners), and c) consumption inequality (how the total sum of money spent by people is distributed among the spenders).
A power inequality is an inequality containing terms of the form a b, where a and b are real positive numbers or variable expressions. They often appear in mathematical olympiads exercises. Examples:
Income inequality in India refers to the unequal distribution of wealth and income among its citizens. According to the CIA World Factbook , the Gini coefficient of India, which is a measure of income distribution inequality, was 35.2 in 2011, ranking 95th out of 157. [ 2 ]
Proof [2]. Since + =, =. A graph = on the -plane is thus also a graph =. From sketching a visual representation of the integrals of the area between this curve and the axes, and the area in the rectangle bounded by the lines =, =, =, =, and the fact that is always increasing for increasing and vice versa, we can see that upper bounds the area of the rectangle below the curve (with equality ...