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

Python3 1==

# importing library

from scipy.stats import poisson 
  
numargs = poisson .numargs 
a, b = 0.2, 0.8
rv = poisson (a, b) 
  
print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4D865848

Code #2 : poisson discrete variates and probability distribution

Python3 1==

import numpy as np 
quantile = np.arange (0.01, 1, 0.1) 

# Random Variates 
R = poisson .rvs(a, b, size = 10) 
print ("Random Variates : \n", R) 

# PDF 
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)

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.

Python3 1==

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))

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

Python3 1==

import matplotlib.pyplot as plt 
import numpy as np 

x = np.linspace(0, 5, 100) 
   
# Varying positional arguments 
y1 = poisson.ppf(x, a, b) 
y2 = poisson.pmf(x, a, b) 
plt.plot(x, y1, "*", x, y2, "r--")