scipy stats.gumbel_r() | Python

scipy.stats.gumbel_r()是一个右偏 Gumbel 连续随机变量，它使用标准格式和一些形状参数定义以完成其规范。

Parameters :
-> q : lower and upper tail probability
-> x : quantiles
-> loc : [optional]location parameter. Default = 0
-> scale : [optional]scale parameter. Default = 1
-> size : [tuple of ints, optional] shape or random variates.
-> moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : Right-Skewed Gumbel continuous random variable

代码 #1：创建右偏 Gumbel 连续随机变量

from scipy.stats import gumbel_r  
  
numargs = gumbel_r  .numargs
[] = [0.7, ] * numargs
rv = gumbel_r ()
  
print ("RV : \n", rv) 

输出 ：

RV : 
 

代码 #2：右偏 Gumbel 随机变量和概率分布

import numpy as np
quantile = np.arange (0.01, 1, 0.1)
   
# Random Variates
R = gumbel_r .rvs(scale = 2,  size = 10)
print ("Random Variates : \n", R)
  
# PDF
R = gumbel_r .pdf(quantile, loc = 0, scale = 1)
print ("\nProbability Distribution : \n", R)

输出 ：

Random Variates : 
 [ 0.55349097 -0.36709655 -0.25581806 -0.81730142  0.28719592 -0.30831366
 -2.69858598 -0.23586469 -1.01965346  6.44132721]

Probability Distribution : 
 [0.36786111 0.36573943 0.36038433 0.35223844 0.34175873 0.32939568
 0.31557754 0.3006994  0.28511631 0.26913983]

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, 3))
print("Distribution : \n", distribution)
  
plot = plt.plot(distribution, rv.pdf(distribution))

输出 ：

Distribution : 
 [0.         0.06122449 0.12244898 0.18367347 0.24489796 0.30612245
 0.36734694 0.42857143 0.48979592 0.55102041 0.6122449  0.67346939
 0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633
 1.10204082 1.16326531 1.2244898  1.28571429 1.34693878 1.40816327
 1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102
 1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714
 2.20408163 2.26530612 2.32653061 2.3877551  2.44897959 2.51020408
 2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102
 2.93877551 3.        ]

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 = gumbel_r .pdf(x, 1, 3)
y2 = gumbel_r .pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

输出 ：