scipy stats.gengamma() | Python
Last Updated :
27 Mar, 2019
scipy.stats.gengamma() is an generalized gamma 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.
-> a, b : shape parameters
-> moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).
Results : generalized gamma continuous random variable
Code #1 : Creating generalized gamma continuous random variable
from scipy.stats import gengamma
numargs = gengamma .numargs
[a, b] = [ 0.7 , ] * numargs
rv = gengamma (a, b)
print ( "RV : \n" , rv)
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Output :
RV :
<scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E39A2A8BE0>
Code #2 : generalized gamma random variates and probability distribution
import numpy as np
quantile = np.arange ( 0.01 , 1 , 0.1 )
R = gengamma.rvs(a, b, scale = 2 , size = 10 )
print ( "Random Variates : \n" , R)
R = gengamma.pdf(a, b, quantile, loc = 0 , scale = 1 )
print ( "\nProbability Distribution : \n" , R)
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Output :
Random Variates :
[1.28899567e-01 6.07031120e-06 7.58807426e-01 1.02689244e+00
2.75752340e-02 8.07943863e-03 4.69774065e-01 2.48110421e-01
4.64544740e-01 7.04892852e+00]
Probability Distribution :
[0.004053 0.04502864 0.08671695 0.12897998 0.17168235 0.21469197
0.25788056 0.30112428 0.34430406 0.38730608]
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 = gengamma.pdf(x, a, 1 , 3 )
y2 = gengamma.pdf(x, a, 1 , 4 )
plt.plot(x, y1, "*" , x, y2, "r--" )
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Output :
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