.. _physics-distributionFunctionMultivariate:

Multivariate Distribution Functions
===================================

Class providing multivariate distribution functions.

**Default implementation:** ``distributionFunctionMultivariateNormal``

Methods
-------

``density`` → ``double precision``
   Return the probability density at ``x``.

   * ``double precision, intent(in ), dimension(:) :: x``

   * ``logical , intent(in ), optional :: logarithmic``

   * ``integer , intent( out), optional :: status``

``cumulative`` → ``double precision``
   Return the cumulative probability between ``xLow``, and ``xHigh``. The cumulative distribution is defined as :math:`P(x_1 < X_1,\ldots,x_N < X_N)` where :math:`\mathbf{X}=`\ ``x``.

   * ``double precision, intent(in ), dimension(:) :: xLow , xHigh``

   * ``logical , intent(in ), optional :: logarithmic``

   * ``integer , intent( out), optional :: status``

.. _physics-distributionFunctionMultivariateNormal:

``distributionFunctionMultivariateNormal``
------------------------------------------

A multivariate normal distribution.

**(Default implementation)**

**Methods**

* ``cumulativeMonteCarlo`` — Compute the cumulative distribution function used Monte Carlo methods.

**Parameters**

* ``[mean]`` — The mean of the multivariate normal distribution.
* ``[covariance]`` — The covariance of the multivariate normal distribution.
* ``[errorAbsolute]`` — The absolute error tolerance in determining the cumulative distribution function.
* ``[errorRelative]`` — The relative error tolerance in determining the cumulative distribution function.
* ``[countTrialsMaximum]`` — The maximum number of trials allowed in Monte Carlo evaluation of the cumulative distribution function.