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 Dirichletdistributed 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
 alphasequence of floats, length k
Parameter of the distribution (length
k
for sample of lengthk
). sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n)
, thenm * n * k
samples are drawn. Default is None, in which case a vector of lengthk
is returned.
 Returns
 samplesndarray,
The drawn samples, of shape
(size, k)
.
 Raises
 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 Dirichletdistributed 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 Dirichletdistributed
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")