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# Python – Inverse Gaussian Distribution in Statistics

scipy.stats.invgauss() is an inverted gauss continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular distribution.

Parameters :

a : shape parameter
c : special case of gengauss. Default equals to c = -1

Code #1 : Creating Inverse Gaussian continuous random variable

 `# importing library``from` `scipy.stats ``import` `invgauss   ``    ` `numargs ``=` `invgauss.numargs ``[a, b] ``=` `[``0.7``, ``0.4``] ``*` `numargs ``rv ``=` `invgauss (a, b) ``    ` `print` `(``"RV : \n"``, rv)  `

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x1a220d7bd0
```

Code #2 : Inverse Gaussian continuous variates and probability distribution

 `import` `numpy as np ``quantile ``=` `np.arange (``0.01``, ``1``) ``     ` `# Random Variates ``R ``=` `invgauss.ppf(``0.01``, a) ``print` `(``"Random Variates : \n"``, R) ``    ` `# PDF ``R ``=` `invgauss.pdf(invgauss.ppf(``0.01``, a), a) ``print` `(``"\nProbability Distribution : \n"``, R) `

Output :

```Random Variates :
0.25801533159920903

Probability Distribution :
0.15984442779701688
```

Code #3 : Graphical Representation.

 `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)) `

Output :

```Distribution :
[0.         0.06122449 0.12244898 0.18367347 0.24489796 0.30612245
0.36734694 0.42857143 0.48979592 0.55102041 0.6122449  0.67346939
0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633
1.10204082 1.16326531 1.2244898  1.28571429 1.34693878 1.40816327
1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102
1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714
2.20408163 2.26530612 2.32653061 2.3877551  2.44897959 2.51020408
2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102
2.93877551 3.        ]
```

Code #4 : Varying Positional Arguments

 `import` `matplotlib.pyplot as plt ``import` `numpy as np ``    ` `x ``=` `np.linspace(``0``, ``5``, ``100``) ``    ` `# Varying positional arguments ``y1 ``=` `invgauss .pdf(x, ``1``, ``3``) ``y2 ``=` `invgauss .pdf(x, ``1``, ``4``) ``plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``) `

Output :