scipy stats.gausshyper() | Python

scipy.stats.gausshyper() is an Gauss hyper-geometric 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.
-> a, b, c, z : shape parameters
-> moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance,
‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : Gauss hyper-geometric continuous random variable

Code #1 : Creating Gauss hypergeometric continuous random variable

from scipy.stats import gausshyper

numargs = gausshyper  .numargs
[a, b, c, z] = [0.7, ] * numargs
rv = gausshyper  (a, b, c, z)

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E399AB5A58>

Code #2 : Gauss hypergeometric random variates and probability distribution.

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

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

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

Output :

Random Variates : 
 [1.45915082 0.58184603 1.91448022 1.23505789 0.9253147  0.36681062
 0.19628827 0.91795248 1.95313724 1.63728124]

Probability Distribution : 
 [0.83983413 0.82838709 0.81749232 0.80714179 0.79731436 0.78798255
 0.77911641 0.77068563 0.76266077 0.75501387]

Code #3 : Graphical Representation.

import numpy as np
import matplotlib.pyplot as plt

distribution = np.linspace(0, np.minimum(rv.dist.b, 3))
print("Distribution : \n", distribution)

plot = plt.plot(distribution, rv.pdf(distribution))

Output :

Distribution : 
 [0.         0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898
 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
 0.36734694 0.3877551  0.40816327 0.42857143 0.44897959 0.46938776
 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
 0.6122449  0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
 0.73469388 0.75510204 0.7755102  0.79591837 0.81632653 0.83673469
 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
 0.97959184 1.        ]

Code #4 : Varying Positional Arguments

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 5, 100)

# Varying positional arguments
y1 = gausshyper .pdf(x, a, z, 1, 3)
y2 = gausshyper .pdf(x, a, z, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :