Python – Negative Binomial Discrete Distribution in Statistics

scipy.stats.nbinom() is a Negative binomial 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 : Negative binomial discrete random variable

Code #1 : Creating Negative binomial discrete random variable

# importing library

from scipy.stats import nbinom

numargs = nbinom .numargs
a, b = 0.2, 0.8
rv = nbinom (a, b)

print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x0000016A4C016208

Code #2 : Negative binomial discrete variates and probability distribution

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

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

# PDF
x = np.linspace(nbinom.ppf(0.01, a, b),
                nbinom.ppf(0.99, a, b), 10)
R = nbinom.ppf(x, 1, 3)
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 [0 0 0 0 0 0 0 0 0 0]

Probability Distribution : 
 [-1. 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))

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)

# Varying positional arguments
y1 = nbinom.ppf(x, a, b)
y2 = nbinom.pmf(x, a, b)
plt.plot(x, y1, "*", x, y2, "r--")

Output :