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. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference.
New code should use the
dirichletmethod of a
default_rng()instance instead; see random-quick-start.
Parameter of the distribution (k dimension for sample of dimension k).
- sizeint 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.
The drawn samples, of shape (size, alpha.ndim).
If any value in alpha is less than or equal to zero
which should be used for new code.
The Dirichlet distribution is a distribution over vectors that fulfil the conditions and .
The probability density function of a Dirichlet-distributed random vector is proportional to
where is a vector containing the positive concentration parameters.
The method uses the following property for computation: let be a random vector which has components that follow a standard gamma distribution, then is Dirichlet-distributed
David McKay, “Information Theory, Inference and Learning Algorithms,” chapter 23, http://www.inference.org.uk/mackay/itila/
Wikipedia, “Dirichlet distribution”, https://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()
>>> import matplotlib.pyplot as plt >>> 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")