scipy stats.gilbrat() | Python

scipy.stats.gilbrat() is an Gilbrat 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 : Gilbrat continuous random variable

Code #1 : Creating Gilbrat continuous random variable

from scipy.stats import gilbrat

numargs = gilbrat .numargs
[] = [0.7, ] * numargs
rv = gilbrat ()

print ("RV : \n", rv)

Output :

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E39A3B4AC8>

Code #2 : Gilbrat random variates and probability distribution

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

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

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

Output :

Random Variates : 
 [0.66090031 1.39027118 1.33876164 1.50366592 5.21419497 5.24225463
 3.98547687 0.30586938 9.11346685 0.93014057]

Probability Distribution : 
 [0.00099024 0.31736749 0.5620854  0.64817773 0.65389139 0.62357239
 0.57879516 0.52988354 0.48170703 0.43645277]

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 = gilbrat.pdf(x, 1, 3)
y2 = gilbrat.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output :