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Python – Log Gamma Distribution in Statistics

  • Last Updated : 10 Jan, 2020

scipy.stats.loggamma() is a log gamma 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 :

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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 : log gamma continuous random variable

Code #1 : Creating log gamma continuous random variable




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

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6AE0588


Code #2 : log gamma continuous variates and probability distribution




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

Output :

Random Variates : 
 3.941580350134656

Probability Distribution : 
 [1.76757240e-27 1.53388070e-24 6.78322725e-22 1.62994246e-19
 2.25532281e-17 1.89389591e-15 1.01217167e-13 3.59400367e-12
 8.81510518e-11 1.54700389e-09]

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

Output :




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