# 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--"``)  `

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