ParaMonte Fortran 2.0.0 Parallel Monte Carlo and Machine Learning LibrarySee the latest version documentation.
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,

$$\large \pi(x | \mu, \sigma) = \frac{1}{x\sigma\sqrt{2\pi}}\exp\bigg( -\frac{\big(\log(x) - \mu\big)^2}{2\sigma^2} \bigg) ~,~ x \in (0, +\infty) ~.$$

The CDF of the Lognormal distribution is defined with the two location and scale parameters $$(\mu \in (-\infty, +\infty), \sigma > 0)$$ as,

$$\large \mathrm{CDF}(x | \mu, \sigma) = \frac{1}{2} \bigg[ 1 + \mathrm{erf} \bigg( \frac{\log(x) - \mu}{\sigma\sqrt{2}} \bigg) \bigg] ~,~ x \in (0, +\infty) ~.$$

Test:
test_pm_distLogNorm

Final Remarks

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

## ◆ MODULE_NAME

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

Definition at line 59 of file pm_distLogNorm.F90.