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Bernoulli Distribution
======================

Generates Bernoulli distributed random numbers.

Details
*******

Bernoulli random number generator fills the :math:`n \times p` numeric table with
Bernoulli distributed values with the :math:`p` probability of success on a single trial, where :math:`p \in R`,
:math:`0 \leq p \leq 1`.

A variate is called Bernoulli distributed if after a trial it is equal to :math:`1`
with the probability of success :math:`p` and to :math:`0` with the probability :math:`1 - p`.
The probability distribution is given by:

.. math::
    p\{x = 1\} = p

.. math::
    p\{x = 0\} = 1 - p

The cumulative distribution function is as follows:

.. math::
    F_p(x) =
    \begin{cases}
      0, & x < 0 \\
		  1 - p, & 0 \leq x < 1, x \in \mathbb{R} \\
      1, & x \geq 1
    \end{cases}

Batch Processing
****************

.. rubric:: Algorithm Parameters

Bernoulli distribution algorithm has the following parameters in addition to the common parameters specified in :ref:`distributions`:

.. tabularcolumns::  |\Y{0.15}|\Y{0.15}|\Y{0.7}|

.. list-table:: Algorithm Parameters for Bernoulli Distribution (Batch Processing)
   :header-rows: 1
   :widths: 10 10 60
   :align: left
   :class: longtable

   * - Parameter
     - Default Value
     - Description
   * - ``algorithmFPType``
     - ``float``
     - The floating-point type that the algorithm uses for intermediate computations. Can be ``float`` or ``double``.
   * - ``method``
     - ``defaultDense``
     - Performance-oriented computation method, the only method supported by the algorithm.
   * - ``p``
     - Not applicable
     - Success probability of a trial, required parameter.

Examples
********

.. tabs::

  .. tab:: Python*

    Batch Processing:

    - :daal4py_example:`distributions_bernoulli_batch.py`

Performance Considerations
**************************

To get the best overall performance when using the Bernoulli distribution random number generator,
provide the 32-bit signed integer homogeneous numeric table constructed with enabled equal features.

.. include:: ../../../opt-notice.rst