scipy stats.arcsine() | Python

scipy.stats.arcsine() is an arcsine continuous random variable that is defined with a standard format and some shape parameters to complete its specification.

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 : arcsine continuous random variable

Code #1 : Creating arcsine continuous random variable

# importing scipy
from scipy.stats import arcsine

numargs = arcsine.numargs
[ ] = [0.6, ] * numargs
rv = arcsine()

print ("RV : \n", rv)

Output :

RV :  
<scipy.stats._distn_infrastructure.rv_frozen object at 0x0000029484D796D8>

Code #2 : arcsine random variates and probability distribution function.

quantile = np.arange (0.01, 1, 0.1)

# Random Variates
R = arcsine.rvs(scale = 2,  size = 10)
print ("Random Variates : \n", R)

# PDF
R = arcsine.pdf(x = quantile, scale = 2)
print ("\nProbability Distribution : \n", R)

Output:

Random Variates : 
 [1.17353658 1.96350916 1.73419819 0.71255312 0.28760466 1.54410451
 1.9644408  0.35014597 0.26798525 0.24599504]

Probability Distribution : 
 [2.25643896 0.69810843 0.51917523 0.43977033 0.39423905 0.3651505
 0.34568283 0.33260295 0.32421577 0.31960693]

Code #3 : Graphical Representation.

# libraries
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.         0.02040816 0.04081633 0.06122449 0.08163265 0.10204082
 0.12244898 0.14285714 0.16326531 0.18367347 0.20408163 0.2244898
 0.24489796 0.26530612 0.28571429 0.30612245 0.32653061 0.34693878
 0.36734694 0.3877551  0.40816327 0.42857143 0.44897959 0.46938776
 0.48979592 0.51020408 0.53061224 0.55102041 0.57142857 0.59183673
 0.6122449  0.63265306 0.65306122 0.67346939 0.69387755 0.71428571
 0.73469388 0.75510204 0.7755102  0.79591837 0.81632653 0.83673469
 0.85714286 0.87755102 0.89795918 0.91836735 0.93877551 0.95918367
 0.97959184 1.        ]

Code #4: Varying Location and Scale

from scipy.stats import arcsine
import matplotlib.pyplot as plt
import numpy as np
a = 2
b = 2
x = np.linspace(0, np.minimum(rv.dist.b, 3))

# Varying location and scale
y1 = arcsine.pdf(x, -0.1, .8)
y2 = arcsine.pdf(x, -3.25, 3.25)
plt.plot(x, y1, "*", x, y2, "r--")