# # U.S. Income Distribution # # From: # # http://quickfacts.census.gov/qfd/states/00000.html # http://bber.unm.edu/econ/us-pci.htm # http://en.wikipedia.org/wiki/Log-normal_distribution # # # In 2010: # # U.S. households = 119,927,000 # U.S. real median income per family = $50,831 # U.S. population = 310,106,000 # # 310106000 # --------- = 2.585789689 persons per family # 119927000 # # 50831 # ----------- = $19,658 = per capita median income # 2.585789689 # # 19658 = e^u # # u = 9.886239659 # # U.S. real mean income per capita = $39,791 # # 39791 = e^(9.886239659 + (s^2/2)) # # s = 1.187565894 # # mode income per capita = e^(u - s^2) = $4,798 # # From: # # http://www.census.gov/hhes/www/cpstables/032011/pov/new35_000.htm # # the poverty line, per capita, is between $5791 and $11344, for an # average of $8567.5, (depending on the number of household members.) # set grid show grid # u = 9.886239659 s = 1.187565894 # set title "U.S. Per Capita Income Distribution, 2010" set xlabel "Income Per Capita, Dollars" set ylabel "Fraction of Population" # set label "Poverty = 8657 +/- 2776" at 8657,3.05e-5 set label "Mode = 4798" at 4598,3.46e-5 set label "Median = 19658" at 19658,1.71e-5 set label "Mean = 39791" at 39791,7.10e-6 set label "u = 9.886240\ns = 1.187566" at 60000,3.4e-5 # # set output "us.income.distribution.jpg" plot[0:87013][0:4e-5] (1 / (x * sqrt (2 * pi * (s ** 2)))) * exp (-(((log (x) - u) ** 2) / (2 * (s ** 2)))) title "(1 / (x * sqrt (2 * pi * (s^2)))) * exp (-(((ln (x) - u)^2) / (2 * (s^2))))" with lines # # From: # # http://www.census.gov/hhes/www/cpstables/032011/hhinc/new06_000.htm # # and dividing the Mean Income per Household by 2.585789689 to obtain # the Mean Income per Capita, and, dividing the Number of Households # by 118682 to obtain the fraction; but note that each "bucket" in the # histogram is (by cut -f1 | tsderivative) 1933.645269, requiring that # the second column be divided by 1933.645269. # # set output "us.income.distribution.emperical.jpg" plot[0:87013][0:4e-5] (1 / (x * sqrt (2 * pi * (s ** 2)))) * exp (-(((log (x) - u) ** 2) / (2 * (s ** 2)))) title "(1 / (x * sqrt (2 * pi * (s^2)))) * exp (-(((ln (x) - u)^2) / (2 * (s^2))))" with lines, "us.income.distribution" title "Emperical" with steps # set terminal jpeg font "/usr/share/fonts/truetype/freefont/FreeSans.ttf,10" set output "us.income.distribution.jpg" set output "us.income.distribution.emperical.jpg" set terminal wxt # exit