numpy.random.
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.
Note
New code should use the dirichlet method of a default_rng() instance instead; see random-quick-start.
default_rng()
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
See also
Generator.dirichlet
which should be used for new code.
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.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")
