scipy stats.hypsecant() | Python

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--")

Output: