%feature("docstring") OT::Dirichlet
"Dirichlet distribution.

Available constructors:
    Dirichlet(*theta=[1.0, 1.0]*)

Parameters
----------
theta : sequence of float, :math:`\theta_i > 0, i = 1, \ldots, n+1`
        theta must be at least bidimensional.

Notes
-----
Its probability density function is defined as:

.. math::

    f_{\vect{X}}(\vect{x}) = \frac{\Gamma(|\vect{\theta}|_1)}
                                  {\prod_{j=1}^{n + 1} \Gamma(\theta_j)}
                             \left[1 - \sum_{j=1}^{n} x_j
                                   \right]^{\theta_{n+1} - 1}
                             \prod_{j=1}^n x_j^{\theta_j - 1},
                             \quad \vect{x} \in \Delta(\vect{X})

with :math:`\Delta(\vect{X}) = \{ \vect{x} \in \Rset^n : x_i \geq 0, \sum_{i=1}^n x_i \leq 1, i = 1, \ldots, n \}`
and :math:`\theta_i > 0, i = 1, \ldots, n+1` and where :math:`|\vect{\theta}|_1 = \sum_{i=1}^{n+1} \theta_i`.

Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \Expect{\vect{X}} & = & \Tr{(\theta_i/|\vect{\theta}|_1,
                                     \quad i = 1, \ldots, n)} \\
        \Cov{\vect{X}} & = & \left[- \frac{\theta_i \theta_j}
                                          {|\vect{\theta}|_1^2
                                           (|\vect{\theta}|_1+1)},
                                   \quad i,j = 1, \ldots, n \right]
    \end{eqnarray*}

.. warning::
    The present implementation does not model the :math:`n+1`-th component of
    the Dirichlet distribution as it is fixed:

    .. math::

        X_{n + 1} = 1 - \sum_{i=1}^{n} X_i

See Also
--------
Multinomial

Examples
--------
Create a distribution:

>>> import openturns as ot
>>> distribution = ot.Dirichlet([1.0, 1.0, 1.0])

Draw a sample:

>>> sample = distribution.getSample(5)"

// ---------------------------------------------------------------------

%feature("docstring") OT::Dirichlet::getTheta
"Accessor to the distribution's vector parameter.

Returns
-------
theta : float, :class:`~openturns.Point`"

// ---------------------------------------------------------------------

%feature("docstring") OT::Dirichlet::setTheta
"Accessor to the distribution's vector parameter.

Parameters
----------
theta : float, sequence of float, :math:`\theta_i > 0, i = 1, \ldots, n+1`"
