.. _oneapi-mkl-rng-hypergeometric:

oneapi::mkl::rng::hypergeometric
================================


Generates hypergeometrically distributed random values.


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Description
***********

The ``oneapi::mkl::rng::hypergeometric`` class object is used in the ``oneapi::mkl::rng::generate`` function to provide hypergeometrically distributed random values with lot size ``l``, size of sampling ``s``, and number of marked elements in the lot ``m``, where ``l, m, s∈N∪{0}; l≥ max(s, m)``.


Consider a lot of ``l`` elements comprising ``m`` "marked" and ``l``-``m`` "unmarked" elements. A trial sampling without replacement of exactly ``s`` elements from this lot helps to define the hypergeometric distribution, which is the probability that the group of ``s`` elements contains exactly ``k`` marked elements.


The probability distribution is given by:


.. math::

   P(X = k) = \frac{C_m^k C_{l-m}^{s-k}}{C_l^s}

, ``k``\ ∈ {max(0, ``s`` + ``m`` - ``l``), ..., min(``s``, ``m``)}


The cumulative distribution function is as follows:


.. math::

   F_{l, s, m}(x) =
   \begin{cases}
      0, & x < max (0, s + m - l)\\
      \sum_{k = \max (0, s+m-l)}^{\lfloor x \rfloor}
         \frac{C_m^k C_{l-m}^{s-k}}{C_l^s},
         & max (0, s + m - l) \leq x \leq \min (s, m)\\
      1, & x > \min(s, m)
   \end{cases}



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   * - Product and Performance Information
   * - Performance varies by use, configuration and other factors. Learn more at `https://www.intel.com/PerformanceIndex <https://www.intel.com/PerformanceIndex>`__. Notice revision #20201201


API
***


Syntax
------

.. code-block:: cpp


   template<typename IntType = std::int32_t, typename Method = hypergeometric_method::by_default>
   class hypergeometric {
   public:
   using method_type = Method;
   using result_type = IntType;
   hypergeometric(): hypergeometric(1, 1, 1){}
   explicit hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m);
   explicit hypergeometric(const param_type& pt);
   std::int32_t s() const;
   std::int32_t m() const;
   std::int32_t l() const;
   param_type param() const;
   void param(const param_type& pt);
   };


Devices supported: Host, CPU, and GPU



Include Files
-------------
- ``oneapi/mkl/rng.hpp``


Template Parameters
-------------------

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   * -     ``typename IntType = std::int32_t``
     -     Type of the produced values. The specific values are as follows:

           ``std::int32_t``

           ``std::uint32_t``
   * -     ``typename Method =  oneapi::mkl::rng:: hypergeometric_method:: by_default``
     -     Generation method. The specific values are as follows:

           ``oneapi::mkl::rng::hypergeometric_method::h2pe``

           See brief descriptions of the methods in :ref:`distributions-template-parameter-method`.


Input Parameters
----------------

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   * - Name
     - Type
     - Description
   * - l
     - ``std::int32_t``
     - Lot size of ``l``.
   * - s
     - ``std::int32_t``
     - Size of sampling without replacement.
   * - m
     - ``std::int32_t``
     - Number of marked elements ``m``.