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

This is the derived type for generating test integrand objects of the Probability Density Function of the Lognormal distribution. More...

## Public Member Functions

procedure get => getIntLogNormPDF

Public Member Functions inherited from pm_quadTest::integrand_type
procedure(get_proc), deferred get
The function member returning the value of the unweighted integrand (whether Cauchy/sin/cos/algebraically types of weights) at a specified input point x. More...

## Public Attributes

real(RKH) mu
The location parameter of the Normal distribution. More...

real(RKH) sigma
The scale parameter (standard deviation) of the Lognormal distribution. More...

real(RKH) invSigma
The inverse scale parameter (standard deviation) of the Lognormal distribution. More...

The natural logarithm of the inverse scale parameter (standard deviation) of the Lognormal distribution. More...

real(RKH) lb
The scalar of type real of the highest kind supported by the library RKH, containing the lower limit of integration. More...

real(RKH) ub
The scalar of type real of the highest kind supported by the library RKH, containing the upper limit of integration. More...

real(RKH) integral
The scalar of type real of the highest kind supported by the library RKH, containing the true result of integration. More...

real(RKH), dimension(:), allocatable break
The scalar of type real of the highest kind supported by the library RKH, containing the points of difficulties of integration. More...

type(wcauchy_type), allocatable wcauchy
The scalar of type wcauchy_type, containing the Cauchy singularity of the integrand. More...

character(:, SK), allocatable desc
The scalar allocatable character of default kind SK containing a description of the integrand and integration limits and difficulties. More...

## Detailed Description

This is the derived type for generating test integrand objects of the Probability Density Function of the Lognormal distribution.

The full integrand is defined as,

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

with an integral value of 1.

Parameters
 [in] lb : The input scalar of type real of kind RKH, containing the lower limit of integration. (optional, default = 0) [in] ub : The input scalar of the same type and kind as lb, containing the upper limit of integration. (optional, default = getInfPos(real(0,kind(ub))) [in] mu : The input scalar of the same type and kind as lb, representing the location parameter of the Lognormal distribution. (optional, default = 0) [in] sigma : The input scalar of the same type and kind as lb, representing the scale parameter of the Lognormal distribution. (optional, default = 1.)

Possible calling interfaces

type(intLogNormPDF_type) :: integrand
integrand = intLogNormPDF_type(lb = lb, ub = ub, mu = mu, sigma = sigma)
print *, "description: ", integrand%desc
print *, "lower limit: ", integrand%lb
print *, "upper limit: ", integrand%ub
print *, "Example integrand value: ", integrand%get(x)
This module contains a collection of interesting or challenging integrands for testing or examining t...
This is the derived type for generating test integrand objects of the Probability Density Function of...
integrand_type
Test:

Final Remarks

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1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

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

Definition at line 1271 of file pm_quadTest.F90.

## ◆ get()

Definition at line 1277 of file pm_quadTest.F90.

References pm_kind::RKH.

## ◆ invSigma

The inverse scale parameter (standard deviation) of the Lognormal distribution.

Definition at line 1274 of file pm_quadTest.F90.

The natural logarithm of the inverse scale parameter (standard deviation) of the Lognormal distribution.

Definition at line 1275 of file pm_quadTest.F90.

## ◆ mu

The location parameter of the Normal distribution.

Definition at line 1272 of file pm_quadTest.F90.