numpy.random.mtrand.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 :

alpha : array

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

size : array

Number of samples to draw.

Returns :

samples : ndarray,

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

Notes

System Message: WARNING/2 (X \approx \prod_{i=1}^{k}{x^{\alpha_i-1}_i} )

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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

System Message: WARNING/2 (X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n))

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is Dirichlet distributed.

References

[R150]

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

[R151]

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.

>>> 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")