Python – Laplace Distribution in Statistics

scipy.stats.laplace() is a Laplace continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular distribution.

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 : laplace continuous random variable

Code #1 : Creating laplace continuous random variable

# importing library

from scipy.stats import laplace

numargs = laplace.numargs
a, b = 4.32, 3.18
rv = laplace(a, b)

print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D4DAF708

Code #2 : laplace continuous variates and probability distribution

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

# Random Variates
R = laplace.rvs(a, b)
print ("Random Variates : \n", R)

# PDF
R = laplace.pdf(a, b, quantile)
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 10.613266250400734

Probability Distribution : 
 [1.54667501e-48 1.43452207e-04 1.04508615e-02 4.07873394e-02
 7.56198196e-02 1.04863398e-01 1.26475923e-01 1.41381881e-01
 1.51096956e-01 1.56988338e-01]

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 = laplace .pdf(x, 1, 3)
y2 = laplace .pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :