数学中国 Ww. madio. net 150 The UMAP Journal 29.2(2008) Table A1 financial wealth distributon by household in the US. in 2001, according to Wolff [2004, 301 Top 15 Next 19% Bottom E0% %weh397%515% 88% We also know that O% percent of the population have 0%o of the wealth and the collective population has all the wealth. This give us the boundary We approximate the Lorenz curve using a Bezier spline fit algorithm because of its ability to generate a smooth curve with relatively few data points. The Bezier fit also guarantees that the curve will be convex, as we would expect a Lorenz curve to be. The disadvantage is that the curve does not pass through all the data points Computation of C and C- We compute the weights C, and C using the Lorenz curve, which we denote by L(a). We define C, to be the ratio of the cumulative wealth of the median person in the lowest quartile to the cumulative wealth of the average person. Thus, C. is given by L(a)dr C.=L)d17 Similarly, define C to be the ratio of the cumulative wealth of the median person of the upper quartile to total wealth So C" is given by L(z)dr fr L(r) The Gini Index of L(e) The Gini index is a numerical measure of the distribution of wealth in a country, defined as G=2g-()d=1-2/.(a)d re L(r)is a Lorenz curve. Thus, the Gini index is 1 minus twice the below the Lorenz curve. Perfect equality in wealth corresponds to G=O, Perfectinequality toG = 1. Numerically integration of our function L(a) )gives oL(x)dr≈,2 1 and hence GusA20≈579数学中国ww.madio.net