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scipy stats.erlang() | Python

  • Last Updated : 20 Mar, 2019

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 :

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