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 :
