ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See 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... | |
real(RKH) | logInvSigma |
The natural logarithm of the inverse scale parameter (standard deviation) of the Lognormal distribution. More... | |
Public Attributes inherited from pm_quadTest::integrand_type | |
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... | |
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,
\begin{equation} \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) \end{equation}
with an integral value of 1
.
[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 ⛓
Final Remarks ⛓
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Definition at line 1271 of file pm_quadTest.F90.
procedure pm_quadTest::intLogNormPDF_type::get |
Definition at line 1277 of file pm_quadTest.F90.
References pm_kind::RKH.
real(RKH) pm_quadTest::intLogNormPDF_type::invSigma |
The inverse scale parameter (standard deviation) of the Lognormal distribution.
Definition at line 1274 of file pm_quadTest.F90.
real(RKH) pm_quadTest::intLogNormPDF_type::logInvSigma |
The natural logarithm of the inverse scale parameter (standard deviation) of the Lognormal distribution.
Definition at line 1275 of file pm_quadTest.F90.
real(RKH) pm_quadTest::intLogNormPDF_type::mu |
The location parameter of the Normal distribution.
Definition at line 1272 of file pm_quadTest.F90.
real(RKH) pm_quadTest::intLogNormPDF_type::sigma |
The scale parameter (standard deviation) of the Lognormal distribution.
Definition at line 1273 of file pm_quadTest.F90.