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

Python3

# 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

Python3

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.

Python3

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

Python3

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 :