Python – Power Log-Normal Distribution in Statistics

Last Updated : 10 Jan, 2020

scipy.stats.powerlognorm() is a power log-normal 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 : power log-normal continuous random variable

Code #1 : Creating power log-normal continuous random variable

# importing library 
  
from scipy.stats import powerlognorm  
    
numargs = powerlognorm .numargs  
a, b = 4.32, 3.18
rv = powerlognorm (a, b)  
    
print ("RV : \n", rv)  

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D8295B48

Code #2 : power log-normal continuous variates and probability distribution

import numpy as np  
quantile = np.arange (0.01, 1, 0.1)  
  
# Random Variates  
R = powerlognorm.rvs(a, b)  
print ("Random Variates : \n", R)  
  
# PDF  
R = powerlognorm.pdf(a, b, quantile)  
print ("\nProbability Distribution : \n", R)  

Output :

Random Variates : 
 0.03729334807608579

Probability Distribution : 
 [0.00000000e+000 8.14360522e-126 7.81567440e-037 1.63561014e-018
 8.34970138e-012 1.30638655e-008 7.72704791e-007 9.42026992e-006
 4.87663742e-005 1.52259891e-004]

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.         0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
 0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
 0.48979592 0.53061224 0.57142857 0.6122449  0.65306122 0.69387755
 0.73469388 0.7755102  0.81632653 0.85714286 0.89795918 0.93877551
 0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
 1.2244898  1.26530612 1.30612245 1.34693878 1.3877551  1.42857143
 1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
 1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
 1.95918367 2.        ]

Code #4 : Varying Positional Arguments

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