Python - Non-Central F-Distribution in Statistics

scipy.stats.ncf() is a non-central F distribution continuous random variable. It is inherited from the of generic methods as an instance of the rv_continuous class. It completes the methods with details specific for this particular 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 : non-central F distribution continuous random variable

Code #1 : Creating non-central F distribution continuous random variable

# importing library 
  
from scipy.stats import ncf   
    
numargs = ncf.numargs  
a, b = 4.32, 3.18
rv = ncf(a, b)  
    
print ("RV : \n", rv)   

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D7FA4AC8

Code #2 : non-central F distribution continuous variates and probability distribution

import numpy as np  
quantile = np.arange (0.01, 1, 0.1)  
  
# Random Variates  
R = ncf.rvs(a, b)  
print ("Random Variates : \n", R)  
  
# PDF  
R = ncf.pdf(a, b, quantile)  
print ("\nProbability Distribution : \n", R)  

Output :

Random Variates : 
 4.491293530275984

Probability Distribution : 
 [0.03182343 0.03305119 0.03427159 0.03548422 0.03668876 0.0378848
 0.03907367 0.04025304 0.04142343 0.04258456]

Code #3 : Graphical Representation.

import numpy as np  
import matplotlib.pyplot as plt  
     
distribution = np.linspace(0, np.minimum(rv.dist.b, 3))  
print("Distribution : \n", distribution)  
     
plot = plt.plot(distribution, rv.pdf(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 = ncf .pdf(x, 1, 3)  
y2 = ncf .pdf(x, 1, 4)  
plt.plot(x, y1, "*", x, y2, "r--")  

Output :

My Personal Notes

Python – Non-Central F-Distribution in Statistics

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