scipy.stats.gumbel_l() is an left-skewed Gumbel 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 : left-Skewed Gumbel continuous random variable
Code #1 : Creating left-skewed Gumbel continuous random variable
from scipy.stats import gumbel_l    numargs = gumbel_l .numargs [] = [0.7, ] * numargs rv = gumbel_l ()   print ("RV : \n", rv) |
Output :
RV : <scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E39A283518>
Code #2 : left-skewed Gumbel random variates and probability distribution
import numpy as np quantile = np.arange (0.01, 1, 0.1)    # Random Variates R = gumbel_l.rvs(scale = 2, size = 10) print ("Random Variates : \n", R)   # PDF R = gumbel_l.pdf(quantile, loc = 0, scale = 1) print ("\nProbability Distribution : \n", R) |
Output :
Random Variates : [ 0.55349097 -0.36709655 -0.25581806 -0.81730142 0.28719592 -0.30831366 -2.69858598 -0.23586469 -1.01965346 6.44132721] Probability Distribution : [0.36786111 0.36573943 0.36038433 0.35223844 0.34175873 0.32939568 0.31557754 0.3006994 0.28511631 0.26913983]
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 = gumbel_l .pdf(x, 1, 3) y2 = gumbel_l .pdf(x, 1, 4) plt.plot(x, y1, "*", x, y2, "r--") |
Output :
