scipy stats.frechet_r() | Python
Last Updated :
27 Mar, 2019
scipy.stats.frechet_r() is an Frechet right (or Weibull minimum) 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 : Frechet right continuous random variable
Code #1 : Creating Frechet right continuous random variable
from scipy.stats import frechet_r
numargs = frechet_r .numargs
[a] = [ 0.7 , ] * numargs
rv = frechet_r (a)
print ( "RV : \n" , rv)
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Output :
RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D56769470>
Code #2 : Frechet right random variates and probability distribution.
import numpy as np
quantile = np.arange ( 0.01 , 1 , 0.1 )
R = frechet_r .rvs(a, scale = 2 , size = 10 )
print ( "Random Variates : \n" , R)
R = frechet_r .pdf(a, quantile, loc = 0 , scale = 1 )
print ( "\nProbability Distribution : \n" , R)
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Output :
Random Variates :
[0.74797562 0.45139233 3.17050565 0.83673559 0.04150534 0.04417758
0.08459631 0.58419257 4.88454049 3.68323048]
Probability Distribution :
[0.00525539 0.05776573 0.11006225 0.16196069 0.21328776 0.26388153
0.31359184 0.36228041 0.40982097 0.45609917]
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))
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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 )
y1 = frechet_r .pdf(x, 1 , 3 )
y2 = frechet_r .pdf(x, 1 , 4 )
plt.plot(x, y1, "*" , x, y2, "r--" )
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Output :
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