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.
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 * ksamples are drawn. Default is None, in which case a single value is returned.
samples : ndarray,
The drawn samples, of shape (size, alpha.ndim).
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 is Dirichlet distributed.
[R219] David McKay, “Information Theory, Inference and Learning Algorithms,” chapter 23, http://www.inference.phy.cam.ac.uk/mackay/ [R220] Wikipedia, “Dirichlet distribution”, http://en.wikipedia.org/wiki/Dirichlet_distribution
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) >>> plt.barh(range(20), s, left=s, color='g') >>> plt.barh(range(20), s, left=s+s, color='r') >>> plt.title("Lengths of Strings")