`numpy.random._generator:Generator.beta`

Signature

def beta ( a , b , size = None )

Summary

Draw samples from a Beta distribution.

Extended Summary

The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function

f (x; a, b) = \frac{1}{B ( α , β )} x^{α - 1} (1 - x)^{β - 1},

where the normalization, B, is the beta function,

B (α, β) = \int_{0}^{1} t^{α - 1} (1 - t)^{β - 1} d t .

It is often seen in Bayesian inference and order statistics.

Parameters

a : float or array_like of floats: Alpha, positive (>0).
b : float or array_like of floats: Beta, positive (>0).
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if a and b are both scalars. Otherwise, np.broadcast(a, b).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized beta distribution.

Examples

The beta distribution has mean a/(a+b). If ``a == b`` and both are > 1, the distribution is symmetric with mean 0.5.

rng = np.random.default_rng()
a, b, size = 2.0, 2.0, 10000
sample = rng.beta(a=a, b=b, size=size)

✓

np.mean(sample)

✗

Otherwise the distribution is skewed left or right according to whether ``a`` or ``b`` is greater. The distribution is mirror symmetric. See for example:

a, b, size = 2, 7, 10000
sample_left = rng.beta(a=a, b=b, size=size)
sample_right = rng.beta(a=b, b=a, size=size)
m_left, m_right = np.mean(sample_left), np.mean(sample_right)

✓

print(m_left, m_right)
print(m_left - a/(a+b))
print(m_right - b/(a+b))

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Display the histogram of the two samples:

import matplotlib.pyplot as plt

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plt.hist([sample_left, sample_right],
         50, density=True, histtype='bar')

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plt.show()

✓

Aliases

numpy.random.Generator.beta