gini和便便关系 Gini.doc

gini和便便关系 Gini Gini coefficient From Wikipedia, the free encyclopedia Graphical representation of the Gini coefficient The Gini coefficient is a measure of inequality of a distribution. It is defined as a ratio with values between 0 and 1: the numerator is the area between the Lorenz curve of the distribution and the uniform distribution line; the denominator is the area under the uniform distribution line. It was developed by the Italian statistician Corrado Gini and published in his 1912 paper Variabilit?e mutabilit? (Variability and Mutability). The Gini index is the Gini coefficient expressed as a percentage, and is equal to the Gini coefficient multiplied by 100. (The Gini coefficient is equal to half of the relative mean difference.) The Gini coefficient is often used to measure income inequality. Here, 0 corresponds to perfect income equality (i.e. everyone has the same income) and 1 corresponds to perfect income inequality (i.e. one person has all the income, while everyone else has zero income). The Gini coefficient can also be used to measure wealth inequality. This use requires that no one has a negative net wealth. It is also commonly used for the measurement of discriminatory power of rating systems in the credit risk management. Calculation The Gini coefficient is defined as a ratio of the areas on the Lorenz curve diagram. If the area between the line of perfect equality and Lorenz curve is A, and the area under the Lorenz curve is B, then the Gini coefficient is A/(A+B). Since A+B = 0.5, the Gini coefficient, G = 2A = 1-2B. If the Lorenz curve is represented by the function Y = L(X), the value of B can be found with integration and: In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve. For example: ? For a population with values yi, i = 1 to n, that are indexed in non-decreasing order ( y i ≤ yi+1): ? For a discrete probability function f(y), where yi, i = 1 to n,