method
RandomState.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: |
|
---|---|
Returns: |
|
Raises: |
|
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
[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 |
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")
© 2005–2019 NumPy Developers
Licensed under the 3-clause BSD License.
https://docs.scipy.org/doc/numpy-1.17.0/reference/random/generated/numpy.random.mtrand.RandomState.dirichlet.html