# numpy.random.dirichlet

random.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.

  Note

  New code should use the `dirichlet` method of a `default_rng()` instance instead; please see the Quick Start.

  Parameters
    alpha sequence of floats, length k

      Parameter of the distribution (length `k` for sample of length `k`).

    size int or tuple of ints, optional

      Output shape. If the given shape is, e.g., `(m, n)`, then `m * n * k` samples are drawn. Default is None, in which case a vector of length `k` is returned.

  Returns
    samples ndarray,

      The drawn samples, of shape `(size, k)`.

  Raises
    ValueError

      If any value in `alpha` is less than or equal to zero

  See also

  `random.Generator.dirichlet`

    which should be used for new code.

  Notes

  The Dirichlet distribution is a distribution over vectors \(x\) that fulfil the conditions \(x_i>0\) and \(\sum_{i=1}^k x_i = 1\).

  The probability density function \(p\) of a Dirichlet-distributed random vector \(X\) is proportional to

  \[p(x) \propto \prod_{i=1}^{k}{x^{\alpha_i-1}_i},\]

  where \(\alpha\) is a vector containing the positive concentration parameters.

  The method uses the following property for computation: let \(Y\) be a random vector which has components that follow a standard gamma distribution, then \(X = \frac{1}{\sum_{i=1}^k{Y_i}} Y\) 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.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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