pm_distLogNorm Module Reference

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"

Detailed Description

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:

1. the Probability Density Function (PDF)
2. the Cumulative Distribution Function (CDF)
3. the Random Number Generation from the distribution (RNG)
4. the Inverse Cumulative Distribution Function (ICDF) or the Quantile Function

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}

Test:

test_pm_distLogNorm

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Variable Documentation

MODULE_NAME

character(*, SK), parameter pm_distLogNorm::MODULE_NAME = "@pm_distLogNorm"

Definition at line 59 of file pm_distLogNorm.F90.