Python – 统计学中的玻尔兹曼分布

scipy.stats.boltzmann()是一个玻尔兹曼（截断离散指数）离散随机变量。它作为rv_discrete 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 ：

x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : boltzmann discrete random variable

代码 #1：创建boltzmann 离散随机变量

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

输出 ：

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4C37A988

代码 #2：boltzmann 离散变量和概率分布

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

输出 ：

Random Variates : 
 [0 0 0 0 0 0 0 0 0 0]

Probability Distribution : 
 [-1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]

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, 2)) 
print("Distribution : \n", distribution) 
     
plot = plt.plot(distribution, rv.ppf(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

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

输出 ：