function that calculates a coefficient for a given Data set

Question

Marko Rajkovic 2018-12-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/434025-function-that-calculates-a-coefficient-for-a-given-data-set

编辑： Marko Rajkovic 2018-12-5

Hello everyone, I am trying to write a function that calculates the Gini coefficient. I have two vectors: one is the vector for the perfect equality line and the other is a vector showing different combinations of income and population share. You can se this on the following image

Now I would like to create a function that calculates (the area between the perfect equality line and the lorenz curve) divided by the lower triangel. The more the red line approaches to the black, the coefficient goes close to zero.

Here I have the codes for the upper graph

%for germany in 2010
Germany2010 = [ZeroIncomeGermany(15) LowestIncome20Germany(15) SecondIncome20Germany(15) ThirdIncome20Germany(15) FourthIncome20Germany(15) FifthIncome20Germany(15)]
Germany2010forGini = cumsum(Germany2010)
ShareOfPopulation = [0 20 40 60 80 100]
figure();
PerfectEqualityX = 0:100; 
PerfectEqualityLine = PerfectEqualityX;
plot(PerfectEqualityX,PerfectEqualityLine,'k');
hold on
plot(Populationshare,Germany2010forGini,'r')
xlabel('Population Share')
ylabel('Share of Income')
legend('Perfect Equality','Lorenz Curve','Location','NorthWest')
title('Represantation of Lorentz Curve/Perfect Equality Line: Germany, 2010')
grid on
hold off

Now I know that the following formula delivers the right coefficient

%%GiniGermany2010 = (trapz(PerfectEqualityLine)-trapz(Germany2010forGini)*20)/trapz(PerfectEqualityLine)

I tried with

function [] = GiniCoefficient(x)
%x = Matrix for selected country and year
Gini(x) = (trapz(PerfectEqualityLine)-trapz(x)*20)/trapz(PerfectEqualityLine)
end 

but it doesn't work, can anyone help?