Python – Kolmogorov-Smirnov Distribution in Statistics

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 :