scipy stats.cauchy () | python



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: Generating a continuous random variable Cauchy

# scipy import

from scipy.stats import cauchy

 

numargs = cauchy.numargs

[] = [ 0.6 ,] * numargs

rv = cauchy ()

  

print ( " RV : " , rv) 

Output:

 RV: & lt; scipy.stats._distn_infrastructure.rv_frozen object at 0x000002948548C6D8 & gt; 

Code # 2: Cauchy random variables 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:" , 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: Graphic representation. / p>

import numpy as np

import matplotlib.pyplot as plt

 

distribution = np.linspace ( 0 , np.minimum (rv .dist.b, 5 ))

print ( "Distribution:" , 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: Various Positional Arguments

import matplotlib. pyplot as plt

import numpy as np

 

x = np.linspace ( 0 , 1.0 , 100 )

 
# Various 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: