scipy.stats.erlang() : is an Erlang continuous random variable that is defined with a standard format and some shape parameters to complete its specification. it is a special case of the Gamma distribution.
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 : erlang continuous random variable
Code #1 : Creating erlang continuous random variable
from scipy.stats import erlang numargs = erlang.numargs [a] = [0.6, ] * numargs rv = erlang(a) print ("RV : \n", rv) |
Output :
RV : <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D544FBC88>
Code #2 : erlang random variates and probability distribution.
import numpy as np quantile = np.arange (0.01, 1, 0.1) # Random Variates R = erlang.rvs(a, scale = 2, size = 10) print ("Random Variates : \n", R) # PDF R = erlang.pdf(a, quantile, loc = 0, scale = 1) print ("\nProbability Distribution : \n", R) |
Output :
Random Variates : [5.65708510e+00 5.16045580e+00 1.02056956e-01 3.64349340e-01 5.65593073e+00 2.27100280e+00 9.77623414e-04 2.01994399e-01 8.84331471e-01 2.20817630e+00] Probability Distribution : [0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91]
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
import matplotlib.pyplot as plt import numpy as np x = np.linspace(0, 5, 100) # Varying positional arguments y1 = erlang.pdf(x, 2, 6) y2 = erlang.pdf(x, 1, 4) plt.plot(x, y1, "*", x, y2, "r--") |
Output :
