RandomState.dirichlet()

RandomState.dirichlet(alpha, size=None)

Draw samples from the Dirichlet distribution.

Draw size samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. Dirichlet pdf is the conjugate prior of a multinomial in Bayesian inference.

Parameters:

Parameters:	alpha : array Parameter of the distribution (k dimension for sample of dimension k). 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. Default is None, in which case a single value is returned.
Returns:	samples : ndarray, The drawn samples, of shape (size, alpha.ndim).

alpha : array

Parameter of the distribution (k dimension for sample of dimension k).

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. Default is None, in which case a single value is returned.

Returns:

samples : ndarray,

The drawn samples, of shape (size, alpha.ndim).

Notes

$X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i}$

Uses the following property for computation: for each dimension, draw a random sample y_i from a standard gamma generator of shape alpha_i, then $X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n)$ is Dirichlet distributed.

References

[R143]

David McKay, ?Information Theory, Inference and Learning Algorithms,? chapter 23, http://www.inference.phy.cam.ac.uk/mackay/

[R144]

Wikipedia, ?Dirichlet distribution?, http://en.wikipedia.org/wiki/Dirichlet_distribution

Examples

Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces.

1	`>>> s` `=` `np.random.dirichlet((10,` `5,` `3),` `20).transpose()`

>>> plt.barh(range(20), s[0])
>>> plt.barh(range(20), s[1], left=s[0], color='g')
>>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')
>>> plt.title("Lengths of Strings")

Links:

https://docs.scipy.org/doc/numpy-1.11.0/reference/generated/numpy.random.RandomState.dirichlet.html

doc_NumPy

2025-01-10 15:47:30

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