scipy stats.genextreme() | Python

scipy.stats.genextreme()是一个广义极值连续随机变量，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.
-> a, b, c : shape parameters
-> moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance,
‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : generalized extreme value continuous random variable

对于 a==0

对于 x <= 1/a，a > 0

代码#1：创建广义极值连续随机变量

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

输出 ：

RV : 
 

代码#2：广义极值随机变量。

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

输出 ：

Random Variates : 
 [ 1.0976659  -4.30499477 -1.30818332  1.54664658  1.44268486  1.80027137
  1.52868675  1.8569798   1.36066713 -1.85945751]

Probability Distribution : 
 [0.30397758 0.32272193 0.34399063 0.3683456  0.39653387 0.42957283
 0.46888883 0.51655345 0.57571147 0.65141728]

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.         0.02915452 0.05830904 0.08746356 0.11661808 0.14577259
 0.17492711 0.20408163 0.23323615 0.26239067 0.29154519 0.32069971
 0.34985423 0.37900875 0.40816327 0.43731778 0.4664723  0.49562682
 0.52478134 0.55393586 0.58309038 0.6122449  0.64139942 0.67055394
 0.69970845 0.72886297 0.75801749 0.78717201 0.81632653 0.84548105
 0.87463557 0.90379009 0.93294461 0.96209913 0.99125364 1.02040816
 1.04956268 1.0787172  1.10787172 1.13702624 1.16618076 1.19533528
 1.2244898  1.25364431 1.28279883 1.31195335 1.34110787 1.37026239
 1.39941691 1.42857143]

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

输出 ：