scipy stats.hypsecant() | Python

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scipy.stats.hypsecant() is an hyperbolic secant continuous random variable. to complete its specificaitons it is defined with a standard format and some shape parameters. The probability density is defined in the “standardized” form.

Parameters :

-> α : scale
-> β : shape
-> μ : location

Code #1 : Creating Hyperbolic secant continuous random variable

from scipy.stats import hypsecant   
   
numargs = hypsecant.numargs 
[] = [0.7, 0.4] * numargs 
rv = hypsecant () 
   
print ("RV : \n", rv)  

Output:

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x0000021FB588A160

Code #2 : Hyperbolic secant continuous variates and probability distribution

import numpy as np 
quantile = np.arange (0.01, 1, 0.1) 
    
# Random Variates 
R = hypsecant .rvs(scale = 2,  size = 10) 
print ("Random Variates : \n", R) 
   
# PDF 
R = hypsecant .pdf(quantile, loc = 0, scale = 1) 
print ("\nProbability Distribution : \n", R) 

Output:

Random Variates : 
 [ 0.50120826  0.60225476 -0.38307417  7.15799321 -1.1929279  -2.03152053
 -0.07410646  1.79859597 -3.14724818  2.03731139]

Probability Distribution : 
 [0.31829397 0.31639377 0.31141785 0.30360449 0.2933099  0.28097073
 0.26706289 0.25206321 0.23641852 0.22052427]

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.         0.06122449 0.12244898 0.18367347 0.24489796 0.30612245
 0.36734694 0.42857143 0.48979592 0.55102041 0.6122449  0.67346939
 0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633
 1.10204082 1.16326531 1.2244898  1.28571429 1.34693878 1.40816327
 1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102
 1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714
 2.20408163 2.26530612 2.32653061 2.3877551  2.44897959 2.51020408
 2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102
 2.93877551 3.        ]

Code #4 : Varying Positional Arguments

import matplotlib.pyplot as plt 
import numpy as np 
   
x = np.linspace(0, 5, 100) 
   
# Varying positional arguments 
y1 = hypsecant .pdf(x, 1, 3) 
y2 = hypsecant .pdf(x, 1, 4) 
plt.plot(x, y1, "*", x, y2, "r--") 