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numpy.random.RandomState.dirichlet

method

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 : 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).

Raises:
ValueError

If any value in alpha is less than or equal to zero

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

[1]David McKay, “Information Theory, Inference and Learning Algorithms,” chapter 23, http://www.inference.org.uk/mackay/itila/
[2]Wikipedia, “Dirichlet distribution”, https://en.wikipedia.org/wiki/Dirichlet_distribution

Examples