🫑Python验证厚尾数据遵循幂律分布

统计学是数据科学和分析的基石。它为我们提供了一个强大的工具箱来客观地回答复杂的问题。然而，许多我们最喜欢的统计工具在应用于特定类别的数据（幂律）时变得毫无用处。

统计中的幂函数分布

scipy.stats.powerlaw() 是幂函数连续随机变量。它作为 rv_continuous 类的实例从泛型方法继承。它使用特定于此特定发行版的详细信息来完成方法。

代码片段-1：创建幂函数连续随机变量

# importing library 

from scipy.stats import powerlaw 
	
numargs = powerlaw.numargs 
a, b = 4.32, 3.18
rv = powerlaw(a, b) 
	
print ("RV : \n", rv)

输出：

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D8295B48

代码片段-2：幂函数连续变量和概率分布

import numpy as np 
quantile = np.arange (0.01, 1, 0.1) 

# Random Variates 
R = powerlaw.rvs(a, b) 
print ("Random Variates : \n", R) 

# PDF 
R = powerlaw.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R)

输出：

Random Variates : 
 3.860143037448123

Probability Distribution : 
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]

代码片段-3：图形表示

import numpy as np 
import matplotlib.pyplot as plt 
	
distribution = np.linspace(0, np.minimum(rv.dist.b, 3)) 
print("Distribution : \n", distribution) 
	
plot = plt.plot(distribution, rv.pdf(distribution))

输出：

Distribution : 
 [0.         0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898
 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
 0.36734694 0.3877551  0.40816327 0.42857143 0.44897959 0.46938776
 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
 0.6122449  0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
 0.73469388 0.75510204 0.7755102  0.79591837 0.81632653 0.83673469
 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
 0.97959184 1.        ]

代码片段-4：不同的位置参数

import matplotlib.pyplot as plt 
import numpy as np 
	
x = np.linspace(0, 5, 100) 
	
# Varying positional arguments 
y1 = powerlaw .pdf(x, 1, 3, 5) 
y2 = powerlaw .pdf(x, 1, 4, 4) 
plt.plot(x, y1, "*", x, y2, "r--")

验证厚尾数据符合幂定律示例

在这里，我们将使用Python 库，确定数据集是否真正遵循幂律分布。

Python验证人工数据

Python验证现实数据

源代码

PreviousPython贝叶斯推理和概率规划 NextPython解离散数学

Last updated 12 months ago

import numpy as np quantile = np.arange (0.01, 1, 0.1) # Random Variates R = powerlaw.rvs(a, b) print ("Random Variates : \n", R) # PDF R = powerlaw.pdf(a, b, quantile) print ("\nProbability Distribution : \n", R)

import numpy as np import matplotlib.pyplot as plt distribution = np.linspace(0, np.minimum(rv.dist.b, 3)) print("Distribution : \n", distribution) plot = plt.plot(distribution, rv.pdf(distribution))

Distribution : [0. 0.02040816 0.04081633 0.06122449 0.08163265 0.10204082 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878 0.36734694 0.3877551 0.40816327 0.42857143 0.44897959 0.46938776 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673 0.6122449 0.63265306 0.65306122 0.67346939 0.69387755 0.71428571 0.73469388 0.75510204 0.7755102 0.79591837 0.81632653 0.83673469 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367 0.97959184 1. ]

import matplotlib.pyplot as plt import numpy as np x = np.linspace(0, 5, 100) # Varying positional arguments y1 = powerlaw .pdf(x, 1, 3, 5) y2 = powerlaw .pdf(x, 1, 4, 4) plt.plot(x, y1, "*", x, y2, "r--")