method
Generator.
dirichlet
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.
Parameter of the distribution (k dimension for sample of dimension k).
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.
(m, n, k)
m * n * k
The drawn samples, of shape (size, alpha.ndim).
If any value in alpha is less than or equal to zero
Notes
The Dirichlet distribution is a distribution over vectors
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System Message: WARNING/2 (\sum_{i=1}^k x_i = 1)
The probability density function
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System Message: WARNING/2 (p(x) \propto \prod_{i=1}^{k}{x^{\alpha_i-1}_i}, )
where
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The method uses the following property for computation: let
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System Message: WARNING/2 (X = \frac{1}{\sum_{i=1}^k{Y_i}} Y)
References
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
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.default_rng().dirichlet((10, 5, 3), 20).transpose()
>>> import matplotlib.pyplot as plt >>> 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")
