# numpy.random.Generator.dirichlet¶

method

Generator.dirichlet(alpha, size=None)

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.

Parameters: 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. samples : ndarray, The drawn samples, of shape (size, alpha.ndim). ValueError If any value in alpha is less than or equal to zero

Notes

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

References

 [1] David McKay, “Information Theory, Inference and Learning Algorithms,” chapter 23, http://www.inference.org.uk/mackay/itila/
 [2] 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")


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