Python – ksone Distribution in Statistics

scipy.stats.ksone() is a General Kolmogorov-Smirnov one-sided test that is defined with a standard format and some shape parameters to complete its specification. It is a statistical test for the finite sample size n.

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.
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : ksone continuous random variable

Code #1 : Creating ksone continuous random variable

# importing library

from scipy.stats import ksone

numargs = ksone.numargs
a, b = 4.32, 3.18
rv = ksone(a, b)

print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D530AB48

Code #2 : Ksone continuous variates and probability distribution

import numpy as np
quantile = np.arange (0.01, 1, 0.1)

# Random Variates
R = ksone.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.         0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898
 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
 0.36734694 0.3877551  0.40816327 0.42857143 0.44897959 0.46938776
 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
 0.6122449  0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
 0.73469388 0.75510204 0.7755102  0.79591837 0.81632653 0.83673469
 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
 0.97959184 1.        ]
 

Code #4 : Varying Positional Arguments

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 5, 100)

# Varying positional arguments
y1 = ksone.pdf(x, 1, 3)
y2 = ksone.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :