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

Available constructors:
    Student(*nu=3.0, d=1*)

    Student(*nu, mu, sigma=1.0*)

    Student(*nu, mu, sigma, R*)

Parameters
----------
d : int, :math:`d \geq 1`
    Dimension.
nu : float, :math:`\nu > 0`
    Generalised number degrees of freedom.
mu : float :math:`\mu`, sequence of float, :math:`\vect{\mu} \in \Rset^d`, optional
    If :math:`\nu > 1`: mean.

    If :math:`\nu = 1`: location parameter.

    Default is :math:`\vect{\mu} = (0, \dots, 0) \in \Rset^d`.
sigma : float :math:`\sigma`, sequence of float, :math:`\vect{\sigma} \in \Rset^{*d}_+`, optional
    Scale parameter.

    Default is :math:`\vect{\sigma} = (1, \dots, 1) \in \Rset^d`.
R : :class:`~openturns.CorrelationMatrix` :math:`\mat{R} \in \Rset^d \times \Rset^d`, optional
    If :math:`\nu > 2`: correlation matrix.

    If :math:`\nu \leq 2`: generalized correlation matrix.

    Default is :math:`\mat{R} = I_d \in \Rset^d \times \Rset^d`.

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

.. math::

    f_X(x) = \frac{\Gamma \left(\frac{\nu + d}{2}\right)}
                  {(\pi \nu) ^ {\frac{d}{2}} \Gamma \left(\frac{\nu}{2}\right)}
             \frac{\left| \mathrm{det}(\mat{R}) \right| ^ {-1/2}}
                  {\prod_{k = 1} ^ d \sigma_k}
             \left(1 + \frac{\vect{z} ^ t \mat{R} ^ {-1} \vect{z}}{\nu}
             \right) ^ {-\frac{\nu + d}{2}}, \quad x \in \Rset

with :math:`\nu > 0, d \geq 1, \mat{R} \in \Rset^d \times \Rset^d,
\sigma_k > 0, k=1, \dots, d` .

where :math:`\vect{z}=\mat{\Delta}^{-1}\left(\vect{x}-\vect{\mu}\right)`, 
:math:`\mat{\Delta} = \mat{\mathrm{diag}}(\vect{\sigma})` and :math:`\Gamma`
denotes Euler's Gamma function :class:`~openturns.SpecFunc_Gamma`.

Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \vect{\Expect{X}} & = & \vect{\mu} \quad \text{ if }\nu>1\\
        \mat{\Cov{X}} & = & \displaystyle \frac{\nu}{\nu-2}
                            \Tr{\mat{\Delta}}\,\mat{R}\,\mat{\Delta}
                          \quad \text{ if }\nu>2
    \end{eqnarray*}

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

>>> import openturns as ot
>>> distribution = ot.Student(5.0, -0.5, 2.0)

Draw a sample:

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

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%feature("docstring") OT::Student::getMu
"Accessor to the distribution's mean.

Returns
-------
mu : float
    Mean.
    Only defined when the dimension is 1
    (else, use the :func:`getMean()` method inherited from the
    EllipticalDistribution class)."

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

%feature("docstring") OT::Student::getNu
"Accessor to the distribution's generalised number degrees of freedom.

Returns
-------
nu : float
    Generalised number degrees of freedom."

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

%feature("docstring") OT::Student::setMu
"Accessor to the distribution's mean.

Parameters
----------
mu : float
    Mean."

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%feature("docstring") OT::Student::setNu
"Accessor to the distribution's generalised number degrees of freedom.

Parameters
----------
nu : float, :math:`\nu > 0`
    Generalised number degrees of freedom."


