scipy.stats.chi2() | Python

scipy.stats.chi2() is an chi square continuous random variable that is defined with a standard format and some shape parameters to complete its specification.

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 : chi squared continuous random variable

Code #1 : Creating chi squared continuous random variable

# importing scipy
from scipy.stats import chi2

numargs = chi2.numargs
[a] = [0.6, ] * numargs
rv = chi2(a)

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000029485196DD8>

Code #2 : chi2 random variates and probability distribution function.

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

# Random Variates
R = chi2.rvs(a, scale = 2,  size = 10)
print ("Random Variates : \n", R)

# PDF
R = chi2.pdf(a, quantile, loc = 0, scale = 1)
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 [6.20115012e-01 4.82717678e-01 1.43760444e-02 1.19755537e+00
 3.00093606e-05 6.11268950e-01 5.99940774e-01 3.20509994e-01
 1.94220599e-01 6.63225404e-01]

Probability Distribution : 
 [0.00615404 0.06544849 0.12034254 0.1704933  0.21568622 0.25581903
 0.29088625 0.32096438 0.34619796 0.36678666]
 

Code #3 : Graphical Representation.

import numpy as np
import matplotlib.pyplot as plt

distribution = np.linspace(0, np.minimum(rv.dist.b, 5))
print("Distribution : \n", distribution)

plot = plt.plot(distribution, rv.pdf(distribution))

Output :

Distribution : 
 [0.         0.10204082 0.20408163 0.30612245 0.40816327 0.51020408
 0.6122449  0.71428571 0.81632653 0.91836735 1.02040816 1.12244898
 1.2244898  1.32653061 1.42857143 1.53061224 1.63265306 1.73469388
 1.83673469 1.93877551 2.04081633 2.14285714 2.24489796 2.34693878
 2.44897959 2.55102041 2.65306122 2.75510204 2.85714286 2.95918367
 3.06122449 3.16326531 3.26530612 3.36734694 3.46938776 3.57142857
 3.67346939 3.7755102  3.87755102 3.97959184 4.08163265 4.18367347
 4.28571429 4.3877551  4.48979592 4.59183673 4.69387755 4.79591837
 4.89795918 5.        ]

Code #4 : Varying Positional Arguments

import matplotlib.pyplot as plt
import numpy as np

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

# Varying positional arguments
y1 = chi2.pdf(x, 1, 6)
y2 = chi2.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :