scipy stats.erlang () | python

scipy.stats.erlang (): is a continuous random Erlang variable that is defined by a standard format and some form parameters to complete its specification. this 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: Generating a continuous random variable Erlang

from scipy.stats import erlang 

 

numargs = erlang.numargs

[a] = [ 0.6 ,] * numargs

rv = erlang (a)

  

 print ( "RV:" , rv) 

Output:

 RV : & lt; scipy.stats._distn_infrastructure.rv_frozen object at 0x0000018D544FBC88 & gt; 

Code # 2: Erlang Random Variables and Probability Distribution.

Output:

 Random Variates: [5.65708510e + 00 5.16045580e + 00 1.02056956e-01 3.64349340 e-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, 0.8 1, 0.91] 

Code # 3: Graphic representation.

import numpy as np

quantile = np.arange ( 0.01 , 1 , 0.1 )

 
# Random Variants

R = erlang.rvs (a, scale = 2 , size = 10 )

print ( "Random Variates:" , R)

 
# PDF

R = erlang.pdf (a, quantile, loc = 0 , scale = 1 )

print ( "Probability Distribution:" , R)

import numpy as np

import matplotlib.pyplot as plt

 

distribution = np.linspace ( 0 , np.minimum (rv.dist.b , 5 ))

print ( "Distribution:" , distribution)

 

plot = plt.plot (distribution, rv.pdf (distribution)) < / p>

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: Various Positional Arguments

import matplotlib. pyplot as plt

import numpy as np

 

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

 
# Various positional arguments

y1 = erlang.pdf (x, 2 , 6 )

y2 = erlang.pdf (x , 1 , 4 )

plt.plot (x, y1, " * " , x, y2, "r--" )

Output: