Python – Poisson Discrete Distribution in Statistics
Last Updated :
10 Jan, 2020
scipy.stats.poisson() is a poisson discrete random variable. It is inherited from the of generic methods as an instance of the rv_discrete class. It completes the methods with details specific for this particular distribution.
Parameters :
x : quantiles
loc : [optional]location parameter. Default = 0
scale : [optional]scale parameter. Default = 1
moments : [optional] composed of letters [‘mvsk’]; ‘m’ = mean, ‘v’ = variance, ‘s’ = Fisher’s skew and ‘k’ = Fisher’s kurtosis. (default = ‘mv’).
Results : poisson discrete random variable
Code #1 : Creating poisson discrete random variable
from scipy.stats import poisson
numargs = poisson .numargs
a, b = 0.2, 0.8
rv = poisson (a, b)
print ("RV : \n", rv)
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Output :
RV :
scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4D865848
Code #2 : poisson discrete variates and probability distribution
import numpy as np
quantile = np.arange (0.01, 1, 0.1)
R = poisson .rvs(a, b, size = 10)
print ("Random Variates : \n", R)
x = np.linspace(poisson.ppf(0.01, a, b),
poisson.ppf(0.99, a, b), 10)
R = poisson.ppf(x, 1, 3)
print ("\nProbability Distribution : \n", R)
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Output :
Random Variates :
[0 0 1 0 1 0 0 1 0 0]
Probability Distribution :
[ 5. nan nan nan nan nan nan nan nan nan]
Code #3 : Graphical Representation.
import numpy as np
import matplotlib.pyplot as plt
distribution = np.linspace(0, np.minimum(rv.dist.b, 2))
print("Distribution : \n", distribution)
plot = plt.plot(distribution, rv.ppf(distribution))
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Output :
Distribution :
[0. 0.04081633 0.08163265 0.12244898 0.16326531 0.20408163
0.24489796 0.28571429 0.32653061 0.36734694 0.40816327 0.44897959
0.48979592 0.53061224 0.57142857 0.6122449 0.65306122 0.69387755
0.73469388 0.7755102 0.81632653 0.85714286 0.89795918 0.93877551
0.97959184 1.02040816 1.06122449 1.10204082 1.14285714 1.18367347
1.2244898 1.26530612 1.30612245 1.34693878 1.3877551 1.42857143
1.46938776 1.51020408 1.55102041 1.59183673 1.63265306 1.67346939
1.71428571 1.75510204 1.79591837 1.83673469 1.87755102 1.91836735
1.95918367 2. ]
Code #4 : Varying Positional Arguments
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0, 5, 100)
y1 = poisson.ppf(x, a, b)
y2 = poisson.pmf(x, a, b)
plt.plot(x, y1, "*", x, y2, "r--")
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Output :
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