flopscope.numpy.random.Generator.beta

fnp.random.Generator.beta(self, a, b, size=None)

Draw samples from a Beta distribution.

Adapted from NumPy docs np.random.Generator.beta

Arearandom

Typecounted

Cost

\text{numel}(\text{output})

Flopscope Context

Beta distribution; cost = numel(output).

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(\alpha, \beta)} x^{\alpha - 1} (1 - x)^{\beta - 1},

where the normalization, B, is the beta function,

B(\alpha, \beta) = \int_0^1 t^{\alpha - 1} (1 - t)^{\beta - 1} dt.

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, flops.broadcast(a, b).size samples are drawn.

Returns

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

References

footnote

1

Wikipedia, "Beta distribution",
https://en.wikipedia.org/wiki/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 = flops.random.default_rng()
>>> a, b, size = 2.0, 2.0, 10000
>>> sample = rng.beta(a=a, b=b, size=size)
>>> flops.mean(sample)
0.5047328775385895  # may vary

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 = flops.mean(sample_left), flops.mean(sample_right)
>>> print(m_left, m_right)
0.2238596793678923 0.7774613834041182  # may vary
>>> print(m_left - a/(a+b))
0.001637457145670096  # may vary
>>> print(m_right - b/(a+b))
-0.0003163943736596009  # may vary

Display the histogram of the two samples:

>>> import matplotlib.pyplot as plt
>>> plt.hist([sample_left, sample_right],
... 50, density=True, histtype='bar')
>>> plt.show()