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 Lognormal distribution. More...
Data Types | |
type | distLogNorm_type |
This is the derived type for signifying distributions that are of type Lognormal as defined in the description of pm_distLogNorm. More... | |
interface | getLogNormCDF |
Generate and return the Cumulative Distribution Function (CDF) of the univariate Lognormal distribution. More... | |
interface | getLogNormLogPDF |
Generate the natural logarithm of probability density function (PDF) of the univariate Lognormal distribution. More... | |
interface | setLogNormCDF |
Generate and return the Cumulative Distribution Function (CDF) of the univariate Lognormal distribution. More... | |
interface | setLogNormLogPDF |
Generate the natural logarithm of probability density function (PDF) of the univariate Lognormal distribution. More... | |
Variables | |
character(*, SK), parameter | MODULE_NAME = "@pm_distLogNorm" |
This module contains classes and procedures for computing various statistical quantities related to the Lognormal distribution.
Specifically, this module contains routines for computing the following quantities of the Lognormal distribution:
The PDF of the Lognormal distribution is defined with the two location and scale parameters \((\mu \in (-\infty, +\infty), \sigma > 0)\) as,
\begin{equation} \large \pi(x | \mu, \sigma) = \frac{1}{x\sigma\sqrt{2\pi}}\exp\bigg( -\frac{\big(\log(x) - \mu\big)^2}{2\sigma^2} \bigg) ~,~ x \in (0, +\infty) ~. \end{equation}
The CDF of the Lognormal distribution is defined with the two location and scale parameters \((\mu \in (-\infty, +\infty), \sigma > 0)\) as,
\begin{equation} \large \mathrm{CDF}(x | \mu, \sigma) = \frac{1}{2} \bigg[ 1 + \mathrm{erf} \bigg( \frac{\log(x) - \mu}{\sigma\sqrt{2}} \bigg) \bigg] ~,~ x \in (0, +\infty) ~. \end{equation}
Final Remarks ⛓
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character(*, SK), parameter pm_distLogNorm::MODULE_NAME = "@pm_distLogNorm" |
Definition at line 59 of file pm_distLogNorm.F90.