scipy stats.chi() | Python

Last Updated : 20 Mar, 2019
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 Python3 
# 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. Python3 1== 
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. Python3 
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 Python3 1== 
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 :
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