ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
This module contains classes and procedures for computing various statistical quantities related to the MultiVariate Normal (MVN) distribution. More...
Data Types | |
type | distMultiNorm_type |
This is the derived type for signifying distributions that are of type MultiVariate Normal (MVN) as defined in the description of pm_distMultiNorm. More... | |
interface | getMultiNormLogPDF |
Generate and return the natural logarithm of the Probability Density Function (PDF) of the MultiVariate Normal distribution as defined in the description of pm_distMultiNorm. More... | |
interface | getMultiNormLogPDFNF |
Generate and return the natural logarithm of the normalization coefficient of the Probability Density Function (PDF) of the MultiVariate Normal distribution as defined in the description of pm_distMultiNorm. More... | |
interface | getMultiNormRand |
Generate and return a (collection) of random vector(s) of size ndim from the ndim -dimensional MultiVariate Normal (MVN) distribution, optionally with the specified input mean(1:ndim) and the specified subset of the Cholesky Factorization of the Covariance matrix of the MVN distribution. More... | |
interface | setMultiNormRand |
Return a (collection) of random vector(s) of size ndim from the ndim -dimensional MultiVariate Normal (MVN) distribution, optionally with the specified input mean(1:ndim) and the specified subset of the Cholesky Factorization of the Covariance matrix of the MVN distribution. More... | |
Variables | |
character(*, SK), parameter | MODULE_NAME = "@pm_distMultiNorm" |
This module contains classes and procedures for computing various statistical quantities related to the MultiVariate Normal (MVN) distribution.
Specifically, this module contains routines for computing the following quantities of the MultiVariate Normal distribution:
The PDF of the MVN distribution with the mean vector \(\bu{\mu}\) and covariance matrix \(\bu{\Sigma}\) at a given input point \(X\) is defined as,
\begin{equation} \large \pi\big(\bu{X} ~|~\bu{\mu}, \bu{\Sigma}\big) = \frac{1}{\sqrt{\big| 2\pi\bu{\Sigma} \big|}} ~ \exp\bigg( -\frac{1}{2}(\bu{X}-\bu{\mu})^T ~ \bu{\Sigma}^{-1} ~ (\bu{X}-\bu{\mu}) \bigg) ~, \end{equation}
which is defined if and only if the \(\bu{\Sigma}\) is positive-definite. The term \(\large \frac{1}{\sqrt{\big| 2\pi\bu{\Sigma} \big|}}\) is the Normalization Factor or the Normalization Constant of the MVN PDF whose natural logarithm can be computed via getMultiNormLogPDFNF in this module.
Final Remarks ⛓
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character(*, SK), parameter pm_distMultiNorm::MODULE_NAME = "@pm_distMultiNorm" |
Definition at line 70 of file pm_distMultiNorm.F90.