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scipy stats.foldcauchy() | Python

  • Last Updated : 27 Mar, 2019

scipy.stats.foldcauchy() is an folded Cauchy continuous random variable that is defined with a standard format and some shape parameters to complete its specification.

Parameters :
-> q : lower and upper tail probability
-> a : shape parameters
-> 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 : folded Cauchy continuous random variable

Code #1 : Creating folded Cauchy continuous random variable




from scipy.stats import foldcauchy
  
numargs = foldcauchy.numargs
[a] = [0.7, ] * numargs
rv = foldcauchy(a)
  
print ("RV : \n", rv) 

Output :



RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D55D8E160>

Code #2 : Folded Cauchy random variates and probability distribution function.




import numpy as np
quantile = np.arange (0.01, 1, 0.1)
   
# Random Variates
R = foldcauchy.rvs(a, scale = 2,  size = 10)
print ("Random Variates : \n", R)
  
# PDF
R = foldcauchy.pdf(a, quantile, loc = 0, scale = 1)
print ("\nProbability Distribution : \n", R) 

Output :

Random Variates : 
 [1.7445128  2.82630984 0.81871044 5.19668279 7.81537565 1.67855736
 3.35417067 0.13838753 1.29145462 1.90601065]

Probability Distribution : 
 [0.42727064 0.42832192 0.43080143 0.43385803 0.43622229 0.43639823
 0.43294602 0.42480391 0.41154712 0.3934792 ]
 

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

Output :

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