scipy.stats.cauchy() is an 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
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 : cauchy continuous random variable
Code #1 : Creating cauchy continuous random variable
# importing scipy from scipy.stats import cauchy numargs = cauchy.numargs [] = [0.6, ] * numargs rv = cauchy() print ("RV : \n", rv) |
Output :
RV : <scipy.stats._distn_infrastructure.rv_frozen object at 0x000002948548C6D8>
Code #2 : cauchy random variates and probability distribution function.
import numpy as np quantile = np.arange (0.01, 1, 0.1) import numpy as np import matplotlib.pyplot as plt distribution = np.linspace(0, np.minimum(rv.dist.b, 5)) print("Distribution : \n", distribution) plot = plt.plot(distribution, rv.pdf(distribution)) |
Output :
Random Variates : [ 2.73388202 4.88389383 -4.89271415 4.63864536 -0.36933865 1.51521875 1.43853452 -0.69619917 -0.68358229 4.13179831] Probability Distribution : [0.31827806 0.31450438 0.30486533 0.29040223 0.27250226 0.25260685 0.23198738 0.21162814 0.19220451 0.17412061]
Code #3 : Graphical Representation.
import numpy as np import matplotlib.pyplot as plt distribution = np.linspace(0, np.minimum(rv.dist.b, 5)) print("Distribution : \n", distribution) plot = plt.plot(distribution, rv.pdf(distribution)) |
Output :
Distribution : Distribution : [0. 0.10204082 0.20408163 0.30612245 0.40816327 0.51020408 0.6122449 0.71428571 0.81632653 0.91836735 1.02040816 1.12244898 1.2244898 1.32653061 1.42857143 1.53061224 1.63265306 1.73469388 1.83673469 1.93877551 2.04081633 2.14285714 2.24489796 2.34693878 2.44897959 2.55102041 2.65306122 2.75510204 2.85714286 2.95918367 3.06122449 3.16326531 3.26530612 3.36734694 3.46938776 3.57142857 3.67346939 3.7755102 3.87755102 3.97959184 4.08163265 4.18367347 4.28571429 4.3877551 4.48979592 4.59183673 4.69387755 4.79591837 4.89795918 5. ]
Code #4 : Varying Positional Arguments
import matplotlib.pyplot as plt import numpy as np x = np.linspace(0, 1.0, 100) # Varying positional arguments y1 = cauchy.pdf(x, 2.75, 2.75) y2 = cauchy.pdf(x, 3.25, 3.25) plt.plot(x, y1, "*", x, y2, "r--") |
Output :
