Public
Edited
Dec 10, 2022
populationTotal=0.5*(146748590 + 146171015)
incomeTotal = 62700.8e9
incomeMean = incomeTotal/populationTotal/12
incomeMedian = 27036.4
dataset15 = datasetPure(15)
dataset146 = datasetPure(146)
dataset1465 = datasetPure(1465)
dataset1465[1464]
incomeOfPopulationGroup = function(x) {
return x*populationWithIncome(x)
}
datasetPure = {
function incomeDistribution(nGroups) {
let data = []
let groupPopulation = populationTotal/nGroups
let groupIncomeMin = 1e-12, groupIncomeMax, groupIncomeMean
let groupTotalYearIncome = []
//The function f and its derivative dfdx come in handy for Newtonian iterations
let f = function(groupIncomeMin, groupIncomeMax) {
return integral(populationWithIncome, groupIncomeMin, groupIncomeMax, 1) - groupPopulation
}
let dfdx = function(groupIncomeMax) {
return populationWithIncome(groupIncomeMax)
}
let delta0 = 10000 //initial step
for (let i = 0; i < nGroups; i++) {
if (i < nGroups-1) { //
groupIncomeMax = groupIncomeMin + delta0
let groupIncomeMaxPre = groupIncomeMax
let err = 100
let j = 0
//Newton iterations: Calculating the maximum income difference at which the population size is equal to a given population size.
while (err*err > 0.01) {
groupIncomeMax += -f(groupIncomeMin, groupIncomeMaxPre)/dfdx(groupIncomeMaxPre)
err = groupIncomeMax - groupIncomeMaxPre
groupIncomeMaxPre = groupIncomeMax
j++
if (j>15) {
groupIncomeMax = j + " iterations were not enough, last result: " + groupIncomeMax
groupIncomeMean = j + " iterations were not enough"
break
}
groupTotalYearIncome[i] = integral(incomeOfPopulationGroup, groupIncomeMin, groupIncomeMax, 1)*12
groupIncomeMean = groupTotalYearIncome[i]/12.0/groupPopulation
delta0 = groupIncomeMax - groupIncomeMin
}
} else { //The maximum income can be infinitely large, so we just write that it is very large.
groupTotalYearIncome[i] = incomeTotal
for (let j = 0; j < nGroups - 1; j++) {
groupTotalYearIncome[i] -= groupTotalYearIncome[j]
}
groupIncomeMean = groupTotalYearIncome[i]/12/groupPopulation
groupIncomeMax = 2*groupIncomeMean - groupIncomeMin
}
data.push({population: groupPopulation, incomeMin: groupIncomeMin, incomeMean: groupIncomeMean, incomeMax: groupIncomeMax, populationIncomeYear: groupTotalYearIncome[i]})
groupIncomeMin = groupIncomeMax
}
return data
}
return incomeDistribution
}
integral = function(f, a, b, tol) {
let n = 1
let h = b - a
let sum = []
let i = 1;
let s, result
sum[0] = 0.5*h*(f(a) + f(b))
let err = 10*tol
while ((err > tol)) {
h = h/2
s = 0
for (let j = 1; j <= n; j++) {
s += f(a + (2*j-1)*h)
}
n = 2*n
sum[i] = 0.5*sum[i-1] + h*s
err = Math.abs(sum[i] - sum[i-1])
result = sum[i]
i = i+1
if (i>20) {
result = "integration error"
break
}
}
return result
}
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