Python – Boltzmann Distribution in Statistics

scipy.stats.boltzmann() is a Boltzmann (Truncated Discrete Exponential) discrete random variable. It is inherited from the of generic methods as an instance of the rv_discrete class. It completes the methods with details specific for this particular distribution.

Parameters :

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

Code #1 : Creating boltzmann discrete random variable

# importing library

from scipy.stats import boltzmann

numargs = boltzmann .numargs
a, b = 0.2, 0.8
rv = boltzmann (a, b)

print ("RV : \n", rv)

Output :

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

Code #2 : boltzmann discrete variates and probability distribution

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)

Output :

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

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

Code #3 : Graphical Representation.

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))

Output :

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.        ]
  

Code #4 : Varying Positional Arguments

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--")

Output :