绘制不同年份（非常倾斜的）财富分配的聪明方法？
Smart way to plot (very skewed) wealth distribution across different years?
我有多个数据框（不同年份），看起来像下面的数据框。每个数据框包含每个 id 持有的财富份额（均匀分布在 1000 个单位的 x 轴箱中。因此，例如，如果有 4,000,000 个人，每个箱将按降序表示 4,000 个人的总和）。我想要的是将其绘制在一张图表中。我缺乏创造力，不知道什么是最好的方式来展示不同年份的这些非常倾斜的财富分配...
当我查看 2021 年的数据框时，前 0.1 人拥有所有财富的 92%。因此，当我使用条形图绘制它时，它看起来就像一条垂直直线，如果我使用折线图，它就是一个 L 形图。我在想也许我应该有不同的 x 轴 bin 宽度，而不是在 a 轴上使用 1000 个相同大小的 bin，可能是顶部 0.1%、顶部 0.1-0.5%、顶部 0.5-1%、1- 5%、5-10%、10-20%、...等等
如果有人有好主意，我真的很感激！
x wealth_share_2016
1 0.33430437283205316
2 0.08857907028903435
3 0.05827083476711605
4 0.03862747269456592
5 0.034995688078949164
6 0.025653645763917113
7 0.021026627708501285
8 0.018026751734878957
9 0.01642864468243111
10 0.015728925648574896
11 0.013588290634843092
12 0.01227954727973525
13 0.011382643296594532
14 0.010141965617682762
15 0.008819245941582449
..
1000 0.000000000011221421
x wealth_share_2017
0.0 0.901371131515615
1.0 0.029149650261610725
2.0 0.01448219525035078
3.0 0.00924941242097224
4.0 0.006528547368042855
5.0 0.004915282901262396
6.0 0.0038227195841958007
7.0 0.003202422960559232
8.0 0.0027194902152005056
9.0 0.002256081738439025
10.0 0.001913906326353021
11.0 0.001655920262049755
12.0 0.001497315358785623
13.0 0.0013007783674694787
14.0 0.0011483994993211357
15.0 0.0010006446573525651
16.0 0.0009187314949837794
17.0 0.0008060306765341464
18.0 0.0007121683663280601
19.0 0.0006479765506981805
20.0 0.0006209618807503557
21.0 0.0005522371927723867
22.0 0.0004900821167110386
23.0 0.0004397140637940455
24.0 0.00039311806560654995
25.0 0.0003568253540177216
26.0 0.00033181209459040074
27.0 0.0003194446403240109
28.0 0.0003184084588259308
29.0 0.0003182506069381648
30.0 0.0003148797013444408
31.0 0.0002961487376129427
32.0 0.00027052175379974156
33.0 0.00024743766685454786
34.0 0.0002256857592625916
35.0 0.00020579998427225097
36.0 0.000189038268813506
37.0 0.00017386965729266948
38.0 0.0001613485014690905
39.0 0.0001574132034911388
40.0 0.0001490677750078641
41.0 0.00013790177558791725
42.0 0.0001282878615396144
43.0 0.00012095612436994448
44.0 0.00011214167633915717
45.0 0.00010421673782294511
46.0 9.715626623684205e-05
47.0 9.282271063116496e-05
48.0 8.696571645233427e-05
49.0 8.108410275243205e-05
50.0 7.672762907247785e-05
51.0 7.164556991989368e-05
52.0 6.712091046340094e-05
53.0 6.402983760430654e-05
54.0 6.340827259447476e-05
55.0 6.212579456204865e-05
56.0 6.0479432395632356e-05
57.0 5.871255187231619e-05
58.0 5.6732218205513816e-05
59.0 5.469844909188562e-05
60.0 5.272638831110061e-05
61.0 5.082941624023762e-05
62.0 4.9172657560503e-05
63.0 4.7723292856953955e-05
64.0 4.640794539328976e-05
65.0 4.4830504104868853e-05
66.0 4.33432435988776e-05
67.0 4.17840819038174e-05
68.0 4.0359335324500254e-05
69.0 3.890539627505912e-05
70.0 3.773843593447448e-05
71.0 3.650676651396156e-05
72.0 3.528219096983737e-05
73.0 3.440527767945646e-05
74.0 3.350747980104347e-05
75.0 3.26561659597071e-05
76.0 3.19802966664897e-05
77.0 3.1835209823474306e-05
78.0 3.183429293715699e-05
79.0 3.183429293715699e-05
80.0 3.179465449554639e-05
81.0 3.1754468203569435e-05
82.0 3.1704945367497785e-05
83.0 3.1660515386167146e-05
84.0 3.161204511239972e-05
85.0 3.160031088406889e-05
86.0 3.160031088406889e-05
87.0 3.159054611415194e-05
88.0 3.1527283185355765e-05
89.0 3.1443493604304305e-05
90.0 3.1323353389521874e-05
91.0 3.117894171029721e-05
92.0 3.0954278315859144e-05
93.0 3.057844960395481e-05
94.0 3.014447137763062e-05
95.0 2.9597164606371073e-05
96.0 2.887863910263771e-05
97.0 2.8423195872524498e-05
98.0 2.7793813070448293e-05
99.0 2.7040901735687525e-05
100.0 2.619028564470109e-05
101.0 2.5450004510283205e-05
102.0 2.4855217140189223e-05
103.0 2.403822662596923e-05
104.0 2.3244772756237742e-05
... ...
1000.0 0.000000023425324
在不规则的百分比范围内对这些数据进行分箱是呈现此类分布的常用方法。您可以使用 pd.cut() 和随后的 group_by():
对数据进行分类和聚合
import pandas as pd
import matplotlib.pyplot as plt
#sample data generation
import numpy as np
rng = np.random.default_rng(123)
n = 1000
df = pd.DataFrame({"x": range(n), "wealth_share_2017": np.sort(rng.pareto(a=100, size=n))[::-1]})
df.loc[0, "wealth_share_2017"] = 50
df["wealth_share_2017"] /= df["wealth_share_2017"].sum()
n = len(df)
#define bins in percent
#the last valueis slightly above 100% to ensure that the final bin is included
bins = [0, 0.1, 0.5, 1.0, 10.0, 50.0, 100.01]
#create figure labels for intervals from bins
labels = [f"[{start:.1f}, {stop:.1f})" for start, stop in zip(bins[:-1], bins[1:])]
#categorize data
df["cats"] = pd.cut(df["x"], bins=[n*i/100 for i in bins], include_lowest=True, right=False, labels=labels)
#and aggregate
df_plot = df.groupby(by="cats")["wealth_share_2017"].sum().mul(100)
df_plot.plot.bar(rot=45, xlabel="Income percentile", ylabel="Wealth share (%)", title=df_plot.name)
plt.tight_layout()
plt.show()
我有多个数据框（不同年份），看起来像下面的数据框。每个数据框包含每个 id 持有的财富份额（均匀分布在 1000 个单位的 x 轴箱中。因此，例如，如果有 4,000,000 个人，每个箱将按降序表示 4,000 个人的总和）。我想要的是将其绘制在一张图表中。我缺乏创造力，不知道什么是最好的方式来展示不同年份的这些非常倾斜的财富分配...
当我查看 2021 年的数据框时，前 0.1 人拥有所有财富的 92%。因此，当我使用条形图绘制它时，它看起来就像一条垂直直线，如果我使用折线图，它就是一个 L 形图。我在想也许我应该有不同的 x 轴 bin 宽度，而不是在 a 轴上使用 1000 个相同大小的 bin，可能是顶部 0.1%、顶部 0.1-0.5%、顶部 0.5-1%、1- 5%、5-10%、10-20%、...等等
如果有人有好主意，我真的很感激！
x wealth_share_2016
1 0.33430437283205316
2 0.08857907028903435
3 0.05827083476711605
4 0.03862747269456592
5 0.034995688078949164
6 0.025653645763917113
7 0.021026627708501285
8 0.018026751734878957
9 0.01642864468243111
10 0.015728925648574896
11 0.013588290634843092
12 0.01227954727973525
13 0.011382643296594532
14 0.010141965617682762
15 0.008819245941582449
..
1000 0.000000000011221421
x wealth_share_2017
0.0 0.901371131515615
1.0 0.029149650261610725
2.0 0.01448219525035078
3.0 0.00924941242097224
4.0 0.006528547368042855
5.0 0.004915282901262396
6.0 0.0038227195841958007
7.0 0.003202422960559232
8.0 0.0027194902152005056
9.0 0.002256081738439025
10.0 0.001913906326353021
11.0 0.001655920262049755
12.0 0.001497315358785623
13.0 0.0013007783674694787
14.0 0.0011483994993211357
15.0 0.0010006446573525651
16.0 0.0009187314949837794
17.0 0.0008060306765341464
18.0 0.0007121683663280601
19.0 0.0006479765506981805
20.0 0.0006209618807503557
21.0 0.0005522371927723867
22.0 0.0004900821167110386
23.0 0.0004397140637940455
24.0 0.00039311806560654995
25.0 0.0003568253540177216
26.0 0.00033181209459040074
27.0 0.0003194446403240109
28.0 0.0003184084588259308
29.0 0.0003182506069381648
30.0 0.0003148797013444408
31.0 0.0002961487376129427
32.0 0.00027052175379974156
33.0 0.00024743766685454786
34.0 0.0002256857592625916
35.0 0.00020579998427225097
36.0 0.000189038268813506
37.0 0.00017386965729266948
38.0 0.0001613485014690905
39.0 0.0001574132034911388
40.0 0.0001490677750078641
41.0 0.00013790177558791725
42.0 0.0001282878615396144
43.0 0.00012095612436994448
44.0 0.00011214167633915717
45.0 0.00010421673782294511
46.0 9.715626623684205e-05
47.0 9.282271063116496e-05
48.0 8.696571645233427e-05
49.0 8.108410275243205e-05
50.0 7.672762907247785e-05
51.0 7.164556991989368e-05
52.0 6.712091046340094e-05
53.0 6.402983760430654e-05
54.0 6.340827259447476e-05
55.0 6.212579456204865e-05
56.0 6.0479432395632356e-05
57.0 5.871255187231619e-05
58.0 5.6732218205513816e-05
59.0 5.469844909188562e-05
60.0 5.272638831110061e-05
61.0 5.082941624023762e-05
62.0 4.9172657560503e-05
63.0 4.7723292856953955e-05
64.0 4.640794539328976e-05
65.0 4.4830504104868853e-05
66.0 4.33432435988776e-05
67.0 4.17840819038174e-05
68.0 4.0359335324500254e-05
69.0 3.890539627505912e-05
70.0 3.773843593447448e-05
71.0 3.650676651396156e-05
72.0 3.528219096983737e-05
73.0 3.440527767945646e-05
74.0 3.350747980104347e-05
75.0 3.26561659597071e-05
76.0 3.19802966664897e-05
77.0 3.1835209823474306e-05
78.0 3.183429293715699e-05
79.0 3.183429293715699e-05
80.0 3.179465449554639e-05
81.0 3.1754468203569435e-05
82.0 3.1704945367497785e-05
83.0 3.1660515386167146e-05
84.0 3.161204511239972e-05
85.0 3.160031088406889e-05
86.0 3.160031088406889e-05
87.0 3.159054611415194e-05
88.0 3.1527283185355765e-05
89.0 3.1443493604304305e-05
90.0 3.1323353389521874e-05
91.0 3.117894171029721e-05
92.0 3.0954278315859144e-05
93.0 3.057844960395481e-05
94.0 3.014447137763062e-05
95.0 2.9597164606371073e-05
96.0 2.887863910263771e-05
97.0 2.8423195872524498e-05
98.0 2.7793813070448293e-05
99.0 2.7040901735687525e-05
100.0 2.619028564470109e-05
101.0 2.5450004510283205e-05
102.0 2.4855217140189223e-05
103.0 2.403822662596923e-05
104.0 2.3244772756237742e-05
... ...
1000.0 0.000000023425324
在不规则的百分比范围内对这些数据进行分箱是呈现此类分布的常用方法。您可以使用 pd.cut() 和随后的 group_by():
import pandas as pd
import matplotlib.pyplot as plt
#sample data generation
import numpy as np
rng = np.random.default_rng(123)
n = 1000
df = pd.DataFrame({"x": range(n), "wealth_share_2017": np.sort(rng.pareto(a=100, size=n))[::-1]})
df.loc[0, "wealth_share_2017"] = 50
df["wealth_share_2017"] /= df["wealth_share_2017"].sum()
n = len(df)
#define bins in percent
#the last valueis slightly above 100% to ensure that the final bin is included
bins = [0, 0.1, 0.5, 1.0, 10.0, 50.0, 100.01]
#create figure labels for intervals from bins
labels = [f"[{start:.1f}, {stop:.1f})" for start, stop in zip(bins[:-1], bins[1:])]
#categorize data
df["cats"] = pd.cut(df["x"], bins=[n*i/100 for i in bins], include_lowest=True, right=False, labels=labels)
#and aggregate
df_plot = df.groupby(by="cats")["wealth_share_2017"].sum().mul(100)
df_plot.plot.bar(rot=45, xlabel="Income percentile", ylabel="Wealth share (%)", title=df_plot.name)
plt.tight_layout()
plt.show()