scipy stats.bradford() | Python

scipy.stats.bradford() is an bradford 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 : bradford continuous random variable

Code #1 : Creating bradford continuous random variable

# importing scipy
from scipy.stats import bradford

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

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x00000294853B04A8>

Code #2 : bradford random variates and probability distribution

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

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

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

Output :

Random Variates : 
 [0.30727583 0.22129839 0.27130072 0.19795865 1.66069665 1.93938843
 0.43435698 0.16437308 0.91592562 1.95369029]

Probability Distribution : 
 [1.26897205 1.19754774 1.13373525 1.07637933 1.02454726 0.97747771
 0.93454311 0.89522152 0.85907529 0.82573473]

Code #3 : Graphical Representation.

import numpy as np
import matplotlib.pyplot as plt

distribution = np.linspace(0, np.maximum(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.        ]