Python - Tukey-Lambda Distribution in Statistics

scipy.stats.tukeylambda() is a Tukey-Lambda 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 : Tukey-Lambda continuous random variable 
 

Code #1 : Creating Tukey-Lambda continuous random variable 
 

# importing library

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

Output : 
 

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D9D71F48

Code #2 : Tukey-Lambda continuous variates and probability distribution 
 

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

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

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

Output : 
 

Random Variates : 
 [ 0.21772132 -0.22664155 -1.59857265  2.60861252  3.14751736  2.06655125
  0.62978366  0.28088051 -2.38894301 -1.16725442]

Probability Distribution : 
 [0.  0.  0.  0.  0.  0.  0.  0.5 0.5 0.5]

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 = tukeylambda.pdf(x, a, b) 
y2 = tukeylambda.pdf(x, a, b) 
plt.plot(x, y1, "*", x, y2, "r--") 

Output :