%feature("docstring") OT::LeastSquaresDistributionFactory
"Least squares factory.

Parameters
----------
distribution : :class:`~openturns.Distribution`
    The distribution defining the parametric model :math:`p_{\vect{\theta}}` to be adjusted to data.

Notes
-----
Implements generic least-squares estimation.

Let us denote :math:`(\vect{x}_1, \dots, \vect{x}_n)` the sample, :math:`p_{\vect{\theta}}`
the particular distribution of probability density function we want to fit to the sample,
and :math:`\vect{\theta} \in \Theta \in \Rset^p` its the parameter vector.


The parameters :math:`\vect{\theta}` are numerically optimized so as the
parametric :math:`CDF_{\vect{\theta}}` gets close enough to the empirical :math:`\hat{CDF}`:

.. math::

    \min_{\vect{\theta} \in \Rset} \sum_{i=1}^{n} \left( CDF_{\vect{\theta}}(\vect{x}_i) - \hat{CDF}(\vect{x}_i) \right) ^2

See also
--------
DistributionFactory

Examples
--------
>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal(0.9, 1.7)
>>> sample = distribution.getSample(10)
>>> factory = ot.LeastSquaresDistributionFactory(ot.Normal())
>>> inf_distribution = factory.build(sample)"

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%feature("docstring") OT::LeastSquaresDistributionFactory::setOptimizationAlgorithm
"Accessor to the solver.

Parameters
----------
solver : :class:`~openturns.OptimizationAlgorithm`
    The solver used for numerical optimization of the likelihood."

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

%feature("docstring") OT::LeastSquaresDistributionFactory::getOptimizationAlgorithm
"Accessor to the solver.

Returns
-------
solver : :class:`~openturns.OptimizationAlgorithm`
    The solver used for numerical optimization of the likelihood."

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

%feature("docstring") OT::LeastSquaresDistributionFactory::setOptimizationBounds
"Accessor to the optimization bounds.

Parameters
----------
problem : :class:`~openturns.Interval`
    The bounds used for numerical optimization of the likelihood."

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

%feature("docstring") OT::LeastSquaresDistributionFactory::getOptimizationBounds
"Accessor to the optimization bounds.

Returns
-------
problem : :class:`~openturns.Interval`
    The bounds used for numerical optimization of the likelihood."

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

%feature("docstring") OT::LeastSquaresDistributionFactory::setOptimizationInequalityConstraint
"Accessor to the optimization inequality constraint.

Parameters
----------
inequalityConstraint : :class:`~openturns.Function`
    The inequality constraint used for numerical optimization of the likelihood."

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

%feature("docstring") OT::LeastSquaresDistributionFactory::setKnownParameter
"Accessor to the known parameters.

Parameters
----------
values : sequence of float
    Values of fixed parameters.
indices : sequence of int
    Indices of fixed parameters.

Examples
--------
>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Beta(2.3, 4.5, -1.0, 1.0)
>>> sample = distribution.getSample(10)
>>> factory = ot.LeastSquaresDistributionFactory(ot.Beta())
>>> # set (a,b) out of (r, t, a, b)
>>> factory.setKnownParameter([-1.0, 1.0], [2, 3])
>>> inf_distribution = factory.build(sample)"

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

%feature("docstring") OT::LeastSquaresDistributionFactory::getKnownParameterValues
"Accessor to the known parameters indices.

Returns
-------
values : :class:`~openturns.Point`
    Values of fixed parameters."

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

%feature("docstring") OT::LeastSquaresDistributionFactory::getKnownParameterIndices
"Accessor to the known parameters indices.

Returns
-------
indices : :class:`~openturns.Indices`
    Indices of fixed parameters."