Python – 统计中的 Levy_stable 分布

scipy.stats.levy_stable()是一个 Levy 稳定的连续随机变量。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 : Levy-stable continuous random variable

编程需要懂一点英语

代码 #1：创建 Levy 稳定的 Levy 连续随机变量

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

输出：

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6803648

代码 #2：Levy 稳定的连续变量和概率分布

import numpy as np 
quantile = np.arange (0.03, 2, 0.21) 
  
# Random Variates 
R = levy_stable.rvs(1.8, -0.5, size = 10) 
print ("Random Variates : \n", R) 
  
# PDF 
R = levy_stable.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R)

输出：

Random Variates : 
 [ 1.20654126 -0.56381774 -1.31527459 -0.90027222  0.52535969  0.03076316
 -4.69310302  0.61194358  1.31207992 -0.84552083]

Probability Distribution : 
 [nan nan nan nan nan nan nan nan nan nan]

代码#3：图形表示。

import numpy as np 
import matplotlib.pyplot as plt 
     
distribution = np.linspace(levy_stable.ppf(0.01, 1.8, -0.5), 
                           levy_stable.ppf(0.99, 1.8, -0.5), 100) 
print("Distribution : \n", distribution)

输出：

Distribution : 
 [-4.92358285 -4.8368521  -4.75012136 -4.66339061 -4.57665986 -4.48992912
 -4.40319837 -4.31646762 -4.22973687 -4.14300613 -4.05627538 -3.96954463
 -3.88281389 -3.79608314 -3.70935239 -3.62262164 -3.5358909  -3.44916015
 -3.3624294  -3.27569866 -3.18896791 -3.10223716 -3.01550641 -2.92877567
 -2.84204492 -2.75531417 -2.66858343 -2.58185268 -2.49512193 -2.40839118
 -2.32166044 -2.23492969 -2.14819894 -2.06146819 -1.97473745 -1.8880067
 -1.80127595 -1.71454521 -1.62781446 -1.54108371 -1.45435296 -1.36762222
 -1.28089147 -1.19416072 -1.10742998 -1.02069923 -0.93396848 -0.84723773
 -0.76050699 -0.67377624 -0.58704549 -0.50031475 -0.413584   -0.32685325
 -0.2401225  -0.15339176 -0.06666101  0.02006974  0.10680048  0.19353123
  0.28026198  0.36699273  0.45372347  0.54045422  0.62718497  0.71391571
  0.80064646  0.88737721  0.97410796  1.0608387   1.14756945  1.2343002
  1.32103094  1.40776169  1.49449244  1.58122319  1.66795393  1.75468468
  1.84141543  1.92814618  2.01487692  2.10160767  2.18833842  2.27506916
  2.36179991  2.44853066  2.53526141  2.62199215  2.7087229   2.79545365
  2.88218439  2.96891514  3.05564589  3.14237664  3.22910738  3.31583813
  3.40256888  3.48929962  3.57603037  3.66276112]