星尘。

你的问题不在于numpy.trapz；而在于1)你对完美等式分布的定义，以及2)基尼系数的标准化。

首先，你将完美的平等分配定义为Q5*H5/2，这是五分之一收入和累积百分比(1.0)的一半。我不知道这个数字代表什么。

其次，必须按完全相等分布下的面积进行标准化；即：gini = (area under perfect equality - area under lorenz)/(area under perfect equality)

如果你定义一条面积为1的完美等式曲线，你不必担心这个问题，但如果你定义完美等式曲线时出现错误，这是一个很好的保障。

为了解决这两个问题，我用numpy.linspace定义了完美的等式曲线。这样做的第一个好处是，您可以使用真实发行版的属性以相同的方式定义它。换句话说，不管你用四分位数、五分位数还是十分位数，完全相等的CDF(y_pe，见下文)都会有正确的形状。第二个优点是，计算它的区域也是用numpy.trapz来完成的，这种并行性使代码更易于阅读，并防止错误的计算。import numpy as np

from matplotlib import pyplot as plt

from numpy import trapz

GDP = (653200000000)

A = (0.49 * GDP) / 100 # Poorest 10%

B = (0.59 * GDP) / 100

C = (0.69 * GDP) / 100

D = (0.79 * GDP) / 100

E = (1.89 * GDP) / 100

F = (2.55 * GDP) / 100

G = (5.0 * GDP) / 100

H = (10.0 * GDP) / 100

I = (18.0 * GDP) / 100

J = (60.0 * GDP) / 100 # Richest 10%

# Divide into quintiles and total income within each quintile

Q1 = float(A + B) # lowest quintile

Q2 = float(C + D) # second quintile

Q3 = float(E + F) # third quintile

Q4 = float(G + H) # fourth quintile

Q5 = float(I + J) # fifth quintile

# Calculate the percent of total income in each quintile

T1 = float((100 * Q1) / GDP) / 100

T2 = float((100 * Q2) / GDP) / 100

T3 = float((100 * Q3) / GDP) / 100

T4 = float((100 * Q4) / GDP) / 100

T5 = float((100 * Q5) / GDP) / 100

TR = float(T1 + T2 + T3 + T4 + T5)

# Calculate the cumulative percentage of household income

H1 = float(T1)

H2 = float(T1+T2)

H3 = float(T1+T2+T3)

H4 = float(T1+T2+T3+T4)

H5 = float(T1+T2+T3+T4+T5)

# The y values. Cumulative percentage of incomes

y = np.array([H1,H2,H3,H4,H5])

# The perfect equality y values. Cumulative percentage of incomes.

y_pe = np.linspace(0.0,1.0,len(y))

# Compute the area using the composite trapezoidal rule.

area_lorenz = np.trapz(y, dx=5)

# Calculate the area below the perfect equality line.

area_perfect = np.trapz(y_pe, dx=5)

# Seems to work fine until here.

# Manually calculated Gini using the values given for the areas above

# turns out at .58 which seems reasonable?

Gini = (area_perfect - area_lorenz)/area_perfect

print Gini

plt.plot(y,label='lorenz')

plt.plot(y_pe,label='perfect_equality')

plt.legend()

plt.show()