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Python – Pearson type-3 Distribution in Statistics

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  • Last Updated : 10 Jan, 2020
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scipy.stats.pearson3() is a Pearson type III 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 : pearson type III continuous random variable

Code #1 : Creating pearson type III continuous random variable




# importing library
  
from scipy.stats import pearson3
    
numargs = pearson3.numargs 
a, b = 4.32, 3.18
rv = pearson3(a, b) 
    
print ("RV : \n", rv)  

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D6C55C48

Code #2 : pearson type III continuous variates and probability distribution




import numpy as np 
quantile = np.arange (0.01, 1, 0.1
  
# Random Variates 
R = pearson3.rvs(a, b) 
print ("Random Variates : \n", R) 
  
# PDF 
R = pearson3.pdf(a, b, quantile) 
print ("\nProbability Distribution : \n", R) 

Output :

Random Variates : 
 2.7215696051772347

Probability Distribution : 
 [0.00632525 0.00681964 0.00735457 0.00793359 0.00856061 0.00923989
 0.00997614 0.01077451 0.01164069 0.01258094]

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 = pearson3 .pdf(x, 1, 3, 5
y2 = pearson3 .pdf(x, 1, 4, 4
plt.plot(x, y1, "*", x, y2, "r--"

Output :


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