Python – Rayleigh Distribution in Statistics

scipy.stats.rayleigh() is a Rayleigh continuous random variable. As an instance of the rv_continuous class, the rayleigh object inherits from it a collection of generic methods and completes them with details specific to 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 : Rayleigh continuous random variable

Code #1 : Creating Rayleigh continuous random variable

Python3

# importing library

from scipy.stats import rayleigh

numargs = rayleigh .numargs
a, b = 4.32, 3.18
rv = rayleigh (a, b)

print ("RV : \n", rv)

Output :

RV : 
 scipy.stats._distn_infrastructure.rv_frozen object at 0x000002A9D843A9C8

Code #2 : Rayleigh continuous variates and probability distribution

Python3

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

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

# PDF
R = rayleigh.pdf(a, b, quantile)
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : 
 6.581597763121607

Probability Distribution : 
 [0.00000000e+00 4.48155819e-22 1.03102695e-05 1.37280742e-02
 1.42084729e-01 3.60395757e-01 5.34360887e-01 6.23116939e-01
 6.45372583e-01 6.28111099e-01]

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 = rayleigh .pdf(x, 1, 3, 5)
y2 = rayleigh .pdf(x, 1, 4, 4)
plt.plot(x, y1, "*", x, y2, "r--")

Output: