scipy.stats.expon() | Python

scipy.stats.expon() is an exponential 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 : exponential continuous random variable

Code #1 : Creating exponential continuous random variable

from scipy.stats import expon

numargs = expon.numargs
[ ] = [0.6, ] * numargs
rv = expon( )

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D56531CC0>

Code #2 : exponential random variates and probability distribution.

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

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

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

Output :

Random Variates : 
 [2.50259466e-04 4.32311862e+00 8.22833503e-01 1.63374263e+00
 4.46784023e+00 3.56781485e+00 3.95381396e+00 1.17623772e+00
 3.21834266e-02 4.14778445e+00]

Probability Distribution : 
 [0.99004983 0.89583414 0.81058425 0.73344696 0.66365025 0.60049558
 0.54335087 0.4916442  0.44485807 0.40252422]
 

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

import matplotlib.pyplot as plt
import numpy as np

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

# Varying positional arguments
y1 = expon.pdf(x, 2, 6)
y2 = expon.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :