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Normal Distribution
===================

Generates normally distributed random numbers.

Details
*******

Normal (Gaussian) random number generator fills the input n x p numeric table with Gaussian random numbers with mean α and standard deviation σ, where α, σ∈R and σ > 0. The probability density function is given by:

.. math::
    f_{\alpha, \sigma}(x) = \frac {1}{\sigma \sqrt{2\pi}}\exp(-\frac {(x - a)^2}{2\sigma^2}), -\infty < x < +\infty

The cumulative distribution function is as follows:

.. math::
    F_{\alpha, \sigma}(x) = \int _{-\infty}^{x} \frac {1}{\sigma \sqrt{2\pi}} \exp(-\frac {(y - a)^2}{2\sigma^2})dy, -\infty < x < +\infty

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

.. rubric:: Algorithm Parameters

Normal 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 Normal 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.
       The only method supported so far is the Inverse Cumulative Distribution Function (ICDF) method.
   * - ``a``
     - :math:`0`
     - The mean :math:`\alpha`
   * - ``sigma``
     - :math:`1`
     - The standard deviation :math:`\sigma`

Examples
********

.. tabs::

  .. tab:: Python*

    Batch Processing:

    - :daal4py_example:`distributions_normal_batch.py`