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scipy stats.f() | Python
  • Last Updated : 20 Mar, 2019

scipy.stats.f() is an F 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, b : 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 : F continuous random variable

Code #1 : Creating F continuous random variable




from scipy.stats import f   
  
numargs = f.numargs
[a, b] = [0.6, ] * numargs
rv = f(a, b)
  
print ("RV : \n", rv) 

Output :



RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D566864A8>

Code #2 : exponential F random variates and probability distribution.




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

Output :

Random Variates : 
 [2.77609532e+00 2.55454726e-04 7.77303742e+01 2.61642158e+02
 3.39772973e-01 8.63437666e+02 3.24316832e+02 5.88915362e+06
 1.27105242e+03 7.30691909e-01]

Probability Distribution : 
 [0.00800042 0.06746857 0.10587056 0.13291306 0.15295841 0.16837285
 0.18056559 0.19043041 0.19856155 0.2053691 ]
 

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 = f  .pdf(x, 2, 6)
y2 = f  .pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :

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