scipy stats.beta() | Python

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

[Tex]f(x,α,β)=(Γ(α+β)xα−1(1−x)β−1​)/Γ(α)Γ(β) [/Tex]

where:

• [Tex]α>0 and β>0β>0[/Tex] are the shape parameters of the Beta distribution.
• [Tex]Γ [/Tex]Gamma is the Gamma function.
• [Tex]0≤x≤1.[/Tex]a

This formula describes the Beta distribution, which is a continuous probability distribution defined on the interval [0, 1].

Code #1 : Creating beta continuous random variable

# importing scipy
from scipy.stats import beta

numargs = beta.numargs
[a, b] = [0.6, ] * numargs
rv = beta(a, b)

print("RV : \n", rv)

Output :

RV : <scipy.stats._distn_infrastructure.rv_frozen object at 0x0000029482FCC438>

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

import numpy as np
quantile = np.arange (0.01, 1, 0.1)
 
# Random Variates
R = beta.rvs(a, b, scale = 2,  size = 10)
print ("Random Variates : \n", R)

# PDF
R = beta.pdf(quantile, a, b, loc = 0, scale = 1)
print ("\nProbability Distribution : \n", R)

Output :

Random Variates : [1.47189604 1.47284574 1.84692416 1.0686604 0.32709236 1.96857076 0.00639731 1.97093898 1.34811881 0.34269426] Probability Distribution : [2.62281037 1.04883674 0.84934164 0.76724957 0.73040985 0.72096547 0.73529768 0.77903762 0.8752367 1.1264383 ]

Code #3 : Graphical Representation.

import numpy as np
import matplotlib.pyplot as plt

distribution = np.linspace(0, np.maximum(rv.dist.b, 5))
plot = plt.plot(distribution, rv.pdf(distribution))

Output :

Code #4 : Varying Positional Arguments

from scipy.stats import arcsine
import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 1.0, 100)

# Varying positional arguments
y1 = beta.pdf(x, 2.75, 2.75)
y2 = beta.pdf(x, 3.25, 3.25)
plt.plot(x, y1, "*", x, y2, "r--")

Output :