mars.tensor.random.dirichlet(alpha, size=None, chunk_size=None, gpu=None, dtype=None)[source]

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 * k samples are drawn. Default is None, in which case a single value is returned.

  • chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension

  • gpu (bool, optional) – Allocate the tensor on GPU if True, False as default

  • dtype (data-type, optional) – Data-type of the returned tensor.


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

Return type



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


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

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.



David McKay, “Information Theory, Inference and Learning Algorithms,” chapter 23,


Wikipedia, “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.

>>> import mars.tensor as mt
>>> s = mt.random.dirichlet((10, 5, 3), 20).transpose()
>>> import matplotlib.pyplot as plt
>>> plt.barh(range(20), s[0].execute())
>>> plt.barh(range(20), s[1].execute(), left=s[0].execute(), color='g')
>>> plt.barh(range(20), s[2].execute(), left=(s[0]+s[1]).execute(), color='r')
>>> plt.title("Lengths of Strings")