Python – 统计中的 Tukey-Lambda 分布

scipy.stats.tukeylambda()是一个 Tukey-Lambda 连续随机变量。它作为rv_continuous 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 ：

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 : Tukey-Lambda continuous random variable 
 

代码 #1：创建 Tukey-Lambda 连续随机变量

Python3

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

输出 ：

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D9D71F48

代码 #2：Tukey-Lambda 连续变量和概率分布

Python3

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

输出 ：

Random Variates : 
 [ 0.21772132 -0.22664155 -1.59857265  2.60861252  3.14751736  2.06655125
  0.62978366  0.28088051 -2.38894301 -1.16725442]

Probability Distribution : 
 [0.  0.  0.  0.  0.  0.  0.  0.5 0.5 0.5]

代码#3：图形表示。

Python3

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.         0.04081633 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

Python3

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

输出 ：