Python - 统计中的约翰逊 SB 分布

scipy.stats.johnsonsb()是 Johnson SB 连续随机变量，使用标准格式和一些形状参数定义以完成其规范。

参数 ：

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 : Johnson SB continuous random variable

代码 #1：创建 Johnson SB 连续随机变量

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

输出 ：

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D50286C8

代码 #2：Johnson SB 连续变量和概率分布

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

输出 ：

Random Variates : 
 [0.42212956 0.60876766 0.35494705 0.42892958 0.25316345 0.51872977
 0.2355019  0.44657975 0.54971277 0.36683771]

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

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.         0.02040816 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#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 = johnsonsb .pdf(x, 1, 3) 
y2 = johnsonsb .pdf(x, 1, 4) 
plt.plot(x, y1, "*", x, y2, "r--") 

输出 ：