scipy stats.dgamma() | Python

scipy.stats.dgamma () is an double 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.
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).

Results : double gamma continuous random variable

Code #1 : Creating double gamma continuous random variable

from scipy.stats import chi

numargs = chi.numargs
[a] = [0.6, ] * numargs
rv = chi(a)

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001FDC8AA3940>

Code #2 : double gamma random variates and probability distribution.

import numpy as np
quantile = np.arange (0.01, 1, 0.1)

# Random Variates
R = chi.rvs(a, scale = 2,  size = 10)
print ("Random Variates : \n", R)

# PDF
R = chi.pdf(a, quantile, loc = 0, scale = 1)
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 [-1.95099046 -0.92462647 -0.44728222 -1.02853811  0.26525202  0.33532233
 -1.74580986 -0.02263675  0.02631306  0.01852519]

Probability Distribution : 
 [0.00457609 0.05019958 0.09422768 0.13505809 0.1714982  0.20274293
 0.22833692 0.24812679 0.2622088  0.27087564]
 

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))

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

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import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 5, 100)

# Varying positional arguments
y1 = chi.pdf(x, 1, 6)
y2 = chi.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")