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

Available constructors:
    Normal(*d=1*)

    Normal(*mu, sigma*)

    Normal(*mu, sigma, R*)

    Normal(*mu, Sigma*)

Parameters
----------
d : int, :math:`d \geq 1`
    Dimension.
mu : float :math:`\mu`, sequence of float, :math:`\vect{\mu} \in \Rset^d`, optional
    Mean.

    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`.
Sigma : :class:`~openturns.CovarianceMatrix` :math:`\mat{\Sigma} \in \Rset^d \times \Rset^d`
    Covariance matrix.

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

.. math::

    f_X(x) = \frac{1}
             {\displaystyle (2\pi)^{\frac{n}{2}}
                            (\mathrm{det}\mathbf{\Sigma})^{\frac{1}{2}}}
             \displaystyle exp \left(-\frac{1}{2}\Tr{(x - \mu)}
                                     \mathbf{\Sigma}^{-1}(x - \mu)\right)

with :math:`\Sigma = \Lambda(\sigma) R \Lambda(\sigma)`,
:math:`\Lambda(\sigma) = diag(\sigma)`,
:math:`R` symmetric, definite and positive, :math:`\sigma_i > 0`.

Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \Expect{X} & = & \vect{\mu} \\
        \Var{X} & = & \mat{\Sigma}
    \end{eqnarray*}

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

>>> import openturns as ot
>>> distribution = ot.Normal(0.0, 1.0)

Draw a sample:

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

