数学中国 Ww. madio net Better Lioing through Math 151 Limitations of our Approximation Although we use data from 2001, the distribution of wealth does not change dramatically from year to year. We use only five data points, including the boundary conditions(o, 0) d(1,1) The Bezier curve passes through the boundary points burt not through data point The gini index for financial wealth of households in the u s. in 2001 was 888 / Wol 2004, 30), while our ap n2in combined ha used scant financial wealth("net worth minus net equity in owner-occupied housing WOlff 2004, 51). Davies et al. [2008 have different data(Table A2)for household wealth, which they take more conventionally to include"non financial assets presumably including home equity financial assets and liabilities"[2008, 21 Wealth distribation for famiies in the U.S. in 2001, accoeding to Davies et aL [2008, 4, Table 11. Top 1% Top 5% Top 10% Bottom 50%6 %wea3%%57%%698% 28% Editors Note: Calculation of the Gini Index from Available Data The U.S. Census Bureau publishes wealth and income data by quintiles The income data are published separately for families and for households [2005a: 2005b], while the wealth data are published for households only (2008a). A household includes related family members plus any unrelated people who share the housing unit. The Bureau also publishes Gini indexes for income [2008b: 2007b; 2007a] calculated from the full Lorenz curves, ogether with other measures of inequality [n.d. I The Gini index cannot be approximated from quintile data by using Simpson's rule for an integral, since Simpsons rule requires an even num- ber of intervals. Using the trapezoid rule would underestimate the Gini coeficient because of the concavity of the Lorenz curve. Gerber [2007] gives a simple method suitable to quintile data. For U.S. family income in 2000, the method gives a Gini index of 422, while the index given by the Census Bureau(based on the full Lorenz curve)is, 433. Further information about both the Lorenz curve and Further details about the Lorenz curve and the Gini index are given in a series of UMAP Modules by Schey [19791.数学中国ww.madio.net