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

Available constructors:
    Skellam(*lambda1=1.0, lambda2=1.0*)

Parameters
----------
lambda1 : float, :math:`\lambda_1 > 0`
    First :class:`~openturns.Poisson` distribution's parameter.

lambda2 : float, :math:`\lambda_2 > 0`
    Second :class:`~openturns.Poisson` distribution's parameter.

Notes
-----
The Skellan distribution takes its values in :math:`\Zset`.
It is the distribution of :math:`(X_1 - X_2)` for :math:`(X_1, X_2)` independant
and respectively distributed according to Poisson(:math:`\lambda_i`).

Its probability density function is defined as:

.. math::

    \Prob{X = k} = 2 \Prob{Y = 2 \lambda_1},
                   \quad \forall k \in \Zset

where Y is distributed according to the :class:`~openturns.NonCentralChiSquare`
distribution :math:`\chi^2_{\nu, \delta}`, with :math:`\nu=2(k+1)` and
:math:`\delta=2\lambda_2`.

Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \Expect{X} & = & \lambda_1 - \lambda_2 \\
        \Var{X} & = & \lambda_1 + \lambda_2
    \end{eqnarray*}

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

>>> import openturns as ot
>>> distribution = ot.Skellam(10.0, 5.0)

Draw a sample:

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

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%feature("docstring") OT::Skellam::getLambda1
"Accessor to the first Poisson distribution's parameter :math:`\lambda_1`.

Returns
-------
lambda1 : float
    First Poisson distribution's parameter :math:`\lambda_1`."

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%feature("docstring") OT::Skellam::getLambda2
"Accessor to the second Poisson distribution's parameter :math:`\lambda_2`.

Returns
-------
lambda2 : float
    Second Poisson distribution's parameter :math:`\lambda_2`."

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

%feature("docstring") OT::Skellam::setLambda1
"Accessor to the first Poisson distribution's parameter :math:`\lambda_1`.

Parameters
----------
lambda1 : float, :math:`\lambda_1 >0`
    First Poisson distribution's parameter :math:`\lambda_1`."

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

%feature("docstring") OT::Skellam::setLambda2
"Accessor to the second Poisson distribution's parameter :math:`\lambda_2`.

Parameters
----------
lambda2 : float, :math:`\lambda_2 >0`
    Second Poisson distribution's parameter :math:`\lambda_2`."

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

%feature("docstring") OT::Skellam::setLambda1Lambda2
"Accessor to the Poisson distributions' parameters.

Namely :math:`\lambda_1` and :math:`\lambda_2`.

Parameters
----------
lambda1 : float, :math:`\lambda_1 >0`
    First Poisson distribution's parameter :math:`\lambda_1`.
lambda2 : float, :math:`\lambda_2 >0`
    Second Poisson distribution's parameter :math:`\lambda_2`."
