scipy stats.chi() | Python

scipy.stats.chi() is an chi 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 continuous random variable

Special Cases :

• chi(1, loc, scale) = halfnormal
• chi(2, 0, scale) = rayleigh
• chi(3, 0, scale) : maxwell

Code #1 : Creating chi continuous random variable

# importing scipy
from scipy.stats import chi

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

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x000002948537C6D8>

Code #2 : chi random variates and probability distribution.

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

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

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

Output :

Random Variates : 
 [2.40483665 1.68478304 0.01664071 2.48977805 3.66286843 1.68463842
 0.14434643 0.67812242 0.46190886 1.99973997]

Probability Distribution : 
 [0.01384193 0.14349716 0.25719966 0.35519439 0.43801475 0.50641521
 0.56131243 0.60373433 0.63477687 0.65556791]
 

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 : 
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 = chi.pdf(x, 1, 6)
y2 = chi.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :