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

Available constructors:
    ZipfMandelbrot(*N=1.0, q=0., s=1.0*)

Parameters
----------
N : int, :math:`N > 0`
q : float, :math:`q \geq 0`
s : float, :math:`s > 0`

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

.. math::

    \Prob{X = k} = \frac{1}{(k+q)^s \mathrm{H}(N,q,s)},
                   \quad \forall k \in [1, N]

where :math:`\mathrm{H}(N,q,s)` is the Generalized Harmonic Number:
:math:`\mathrm{H}(N,q,s) = \sum_{i=1}^{N} \frac{1}{(i+q)^s}`.

Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \Expect{X} & =  & \frac{\mathrm{H}_{N,q,s-1}}{\mathrm{H}_{N,q,s}}-q \\
        \Var{X} & = & \frac{\displaystyle \sum_{i=1}^N
                                \frac{(i - \Expect{X})^2}{(i+q)^s}}{\mathrm{H}_{N,q,s}}
    \end{eqnarray*}

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

>>> import openturns as ot
>>> distribution = ot.ZipfMandelbrot(15, 1.2, 2.0)

Draw a sample:

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

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%feature("docstring") OT::ZipfMandelbrot::getN
"Accessor to the parameter :math:`N`.

Returns
-------
N : int"

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%feature("docstring") OT::ZipfMandelbrot::getQ
"Accessor to the parameter :math:`q`.

Returns
-------
q : float"

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%feature("docstring") OT::ZipfMandelbrot::getS
"Accessor to the parameter :math:`s`.

Returns
-------
s : float"

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%feature("docstring") OT::ZipfMandelbrot::setN
"Accessor to the parameter :math:`N`.

Parameters
----------
N : int, :math:`N > 0`"

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%feature("docstring") OT::ZipfMandelbrot::setQ
"Accessor to the parameter :math:`q`.

Parameters
----------
q : float, :math:`q >= 0`"

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%feature("docstring") OT::ZipfMandelbrot::setS
"Accessor to the parameter :math:`s`.

Parameters
----------
s : float, :math:`s > 0`"
