scipy stats.gompertz() | Python

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 : Gompertz (or truncated Gumbel) continuous random variable

from scipy.stats import gompertz 

numargs = gompertz.numargs
[a] = [0.7, ] * numargs
rv = gompertz(a)

print ("RV : \n", rv) 

RV : 
 <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E39A3E2470>

import numpy as np
quantile = np.arange (0.01, 1, 0.1)
 
# Random Variates
R = gompertz.rvs(a, scale = 2,  size = 10)
print ("Random Variates : \n", R)

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

Random Variates : 
 [1.29938059 1.47547887 1.33324567 1.79424061 0.45304378 1.46222247
 1.29260365 0.59989705 3.58467676 1.81226267]

Probability Distribution : 
 [0.01993441 0.19813875 0.34179784 0.45591617 0.54485437 0.61240685
 0.66187043 0.69610503 0.71758726 0.72845776]

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))

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.        ]

import matplotlib.pyplot as plt
import numpy as np

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

# Varying positional arguments
y1 = gompertz.pdf(x, 1, 3)
y2 = gompertz.pdf(x, 1, 4)
plt.plot(x, y1, "*", x, y2, "r--")