scipy stats.chi() | Python

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

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

# importing scipy
from scipy.stats import chi 

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

print ("RV : \n", rv) 

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

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)

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]
 

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))

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.        ]

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--")