scipy stats.cauchy() | Python
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
from scipy.stats import cauchy
numargs = cauchy.numargs
[] = [ 0.6 , ] * numargs
rv = cauchy()
print ( "RV : \n" , rv)
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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))
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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))
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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 )
y1 = cauchy.pdf(x, 2.75 , 2.75 )
y2 = cauchy.pdf(x, 3.25 , 3.25 )
plt.plot(x, y1, "*" , x, y2, "r--" )
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Output :
Last Updated :
20 Mar, 2019
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