scipy stats.foldcauchy() | Python

scipy.stats.foldcauchy()是一个折叠的柯西连续随机变量，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
-> a : shape parameters
-> 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 : folded Cauchy continuous random variable

代码#1：创建折叠柯西连续随机变量

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

输出 ：

RV : 
 

代码#2：折叠柯西随机变量和概率分布函数。

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

输出 ：

Random Variates : 
 [1.7445128  2.82630984 0.81871044 5.19668279 7.81537565 1.67855736
 3.35417067 0.13838753 1.29145462 1.90601065]

Probability Distribution : 
 [0.42727064 0.42832192 0.43080143 0.43385803 0.43622229 0.43639823
 0.43294602 0.42480391 0.41154712 0.3934792 ]
 

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

输出 ：