scipy stats.betaprime() | Python

scipy.stats.betaprime() is an beta prime 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
a, b : shape parameters
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 : beta prime continuous random variable

Code #1 : Creating betaprime continuous random variable

# importing scipy
from scipy.stats import betaprime

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

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000029482FCC438>

Code #2 : betaprime random variates and probability distribution.

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

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

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

Output :

Random Variates : 
 [ 1.59603917  1.92408727  1.2120992   0.34064091  2.68681773 22.99956678
  1.45523032  2.93360219 23.93717261 18.04203815]

Probability Distribution : 
 [2.58128122 0.8832351  0.61488062 0.47835546 0.39160163 0.33053737
 0.28490363 0.24941484 0.22101038 0.1977718 ]
 

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

from scipy.stats import arcsine
import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 1.0, 100)

# Varying positional arguments
y1 = betaprime.pdf(x, 2.75, 2.75)
y2 = betaprime.pdf(x, 3.25, 3.25)
plt.plot(x, y1, "*", x, y2, "r--")

Output :