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

Helper class for defining the Inverse Gamma distribution which is the inverse of a :math:`\Gamma` distribution.

Available constructors:
    InverseGamma(*k, lambda*)

Parameters
----------
k : float, :math:`k > 0`,
    Shape parameter. By default, :math:`k=1`.

lambda : float, :math:`\lambda > 0`.
    Scale parameter. By default, :math:`\lambda=1`.
     

Notes
-----
:math:`X` follows an Inverse Gamma distribution of parameters :math:`(k, \lambda)` means that :math:`\dfrac{1}{X}` follows the :math:`\Gamma(k, \dfrac{1}{\lambda})` distribution, with :math:`k>0` and :math:`\lambda>0`.

Its probability density function is defined as:

.. math::

    f_X(x) = \dfrac{\exp \left( -\dfrac{1}{\lambda x}\right)}{\Gamma(k)\lambda^kx^{k+1}}, \quad x \in [0; +\infty[

with :math:`k >0 , \lambda > 0`.


Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \Expect{X} & = & \dfrac{1}{\lambda(k-1)} \quad \text{if } k>1 \\
        \Var{X} & = &\dfrac{1}{\lambda^2(k-1)^2(k-2)} \quad \text{if } k>2 
    \end{eqnarray*}


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

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

Draw a sample:

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

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%feature("docstring") OT::InverseGamma::getK
"Accessor to the  parameter :math:`k`.

Returns
-------
k : float
    Shape parameter :math:`k`."

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%feature("docstring") OT::InverseGamma::getLambda
"Accessor to the parameter :math:`\lambda`.

Returns
-------
lambda : float
    Scale parameter :math:`\lambda`."

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%feature("docstring") OT::InverseGamma::setK
"Accessor to the distribution's shape parameter :math:`k`.

Parameters
----------
k : float, :math:`k > 0`
    Parameter :math:`k`."

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%feature("docstring") OT::InverseGamma::setLambda
"Accessor to the distribution's scale parameter :math:`\lambda`.

Parameters
----------
lambda : float, :math:`\lambda > 0`
    Parameter :math:`\lambda`."
