Python – Logarithmic Discrete Distribution in Statistics

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scipy.stats.logser() is a Logarithmic (Log-Series, Series) discrete random variable. It is inherited from the of generic methods as an instance of the rv_discrete class. It completes the methods with details specific for this particular distribution.

Parameters :

x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : Logarithmic (Log-Series, Series) discrete random variable

Code #1 : Creating Logarithmic (Log-Series, Series) discrete random variable

# importing library 
  
from scipy.stats import logser  
    
numargs = logser .numargs  
a, b = 0.2, 0.8
rv = logser (a, b)  
    
print ("RV : \n", rv)   

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4C016208

Code #2 : Logarithmic (Log-Series, Series) discrete variates and probability distribution

import numpy as np  
quantile = np.arange (0.01, 1, 0.1)  
  
# Random Variates  
R = logser .rvs(a, b, size = 10)  
print ("Random Variates : \n", R)  
  
# PDF  
x = np.linspace(logser.ppf(0.01, a, b), 
                logser.ppf(0.99, a, b), 10) 
R = logser.ppf(x, 1, 3) 
print ("\nProbability Distribution : \n", R)  

Output :

Random Variates : 
 [1 1 1 1 1 1 1 1 1 1]

Probability Distribution : 
 [nan nan nan nan nan nan nan nan nan nan]

Code #3 : Graphical Representation.

import numpy as np  
import matplotlib.pyplot as plt  
     
distribution = np.linspace(0, np.minimum(rv.dist.b, 2))  
print("Distribution : \n", distribution)  
     
plot = plt.plot(distribution, rv.ppf(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 = logser.ppf(x, a, b)  
y2 = logser.pmf(x, a, b)  
plt.plot(x, y1, "*", x, y2, "r--")  