randomstate.prng.mrg32k3a.dirichlet

randomstate.prng.mrg32k3a.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 – The drawn samples, of shape (size, alpha.ndim).

Return type:

ndarray,

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.phy.cam.ac.uk/mackay/

[2]	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")