Python统计学中的 Yule-Simon 离散分布

scipy.stats.yulesimon()是一个 Yule-Simon 离散随机变量。它作为rv_discrete 类的实例继承自泛型方法。它使用特定于此特定发行版的详细信息来完成方法。

参数：

x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : Yule-Simon discrete random variable

编程需要懂一点英语

代码 #1：创建 Yule-Simon 离散随机变量

# importing library
  
from scipy.stats import yulesimon 
    
numargs = yulesimon .numargs 
a, b = 0.2, 0.8
rv = yulesimon (a, b) 
    
print ("RV : \n", rv)

输出：

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4D865848

代码 #2：Yule-Simon 离散变量和概率分布

import numpy as np 
quantile = np.arange (0.01, 1, 0.1) 
  
# Random Variates 
R = yulesimon .rvs(a, b, size = 10) 
print ("Random Variates : \n", R) 
  
# PDF 
x = np.linspace(yulesimon.ppf(0.01, a, b),
                yulesimon.ppf(0.99, a, b), 10)
R = yulesimon.ppf(x, 1, 3)
print ("\nProbability Distribution : \n", R)

输出：

Random Variates : 
 [5468 3493    5    4   15  416   38   39    8   84]

Probability Distribution : 
 [nan nan nan nan nan nan nan nan nan nan]

代码#3：图形表示。

import numpy as np 
import matplotlib.pyplot as plt 
     
distribution = np.linspace(0, np.minimum(rv.dist.b, 2)) 
print("Distribution : \n", distribution)

输出：

Distribution : 
 [0.         0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
 0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
 0.48979592 0.53061224 0.57142857 0.6122449  0.65306122 0.69387755
 0.73469388 0.7755102  0.81632653 0.85714286 0.89795918 0.93877551
 0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
 1.2244898  1.26530612 1.30612245 1.34693878 1.3877551  1.42857143
 1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
 1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
 1.95918367 2.        ]

代码#4：改变位置参数

import matplotlib.pyplot as plt 
import numpy as np 
  
x = np.linspace(0, 5, 100) 
     
# Varying positional arguments 
y1 = yulesimon.ppf(x, a, b) 
y2 = yulesimon.pmf(x, a, b) 
plt.plot(x, y1, "*", x, y2, "r--")

输出：
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