Python – Inverse Weibull Distribution in Statistics

scipy.stats.invweibull() is an inverted weibull 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 : Inverse weibull continuous random variable

Code #1 : Creating inverted weibull continuous random variable

# importing library
from scipy.stats import invweibull

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

print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D4EAE9C8

Code #2 : inverted weibull continuous variates and probability distribution

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

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

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

Output :

Random Variates : 
 [ 2.46502056 32.97160826  8.65843435  1.21357636  0.22162243  1.05724138
  7.5574935   0.0624836   0.83384033 17.29417907]

Probability Distribution : 
 [0.00613124 0.06733615 0.12799203 0.18757349 0.24553408 0.30131353
 0.35434638 0.40407156 0.44994318 0.49144206]

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

Output :