Python – Kolmogorov-Smirnov Distribution in Statistics

• Last Updated : 10 Jan, 2020

scipy.stats.kstwobign() is Kolmogorov-Smirnov two-sided test for large N test that is defined with a standard format and some shape parameters to complete its specification. It is a statistical test that measures the maximum absolute distance of the theoretical CDF from the empirical CDF.

Parameters :

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.

Results : kstwobign continuous random variable

Code #1 : Creating kstwobign continuous random variable

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

Output :

```RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D54959C8
```

Code #2 : kstwobign continuous variates and probability distribution

 `import` `numpy as np ``quantile ``=` `np.arange (``0.01``, ``1``, ``0.1``) `` ` `# Random Variates ``R ``=` `kstwobign.rvs(a, b, scale ``=` `2``, size ``=` `10``) ``print` `(``"Random Variates : \n"``, R) `

Output :

```Random Variates :
[3.88510141 3.48394857 3.66124797 3.88484201 3.86533511 3.21176073
4.10238585 3.42397866 3.85111721 4.36433596]
```

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 ``=` `kstwobign .pdf(x, ``1``, ``3``) ``y2 ``=` `kstwobign .pdf(x, ``1``, ``4``) ``plt.plot(x, y1, ``"*"``, x, y2, ``"r--"``) `

Output :

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