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 (Truncated) Power/Pareto distribution (hence the name Poweto). More...
Data Types | |
type | distPoweto_type |
This is the derived type for signifying distributions that are of type Poweto as defined in the description of pm_distPoweto. More... | |
interface | getPowetoLogCDF |
Generate and return the natural logarithm of the Cumulative Distribution Function (CDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).More... | |
interface | getPowetoLogCDFNF |
Generate and return the natural logarithm of the normalization factor of the Cumulative Distribution Function (CDF) of the (Truncated) Poweto distribution for the input parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\). More... | |
interface | getPowetoLogPDF |
Generate and return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).More... | |
interface | getPowetoLogPDFNF |
Generate and return the natural logarithm of the normalization factor of the Probability Density Function (PDF) of the (Truncated) Poweto distribution for the input parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\). More... | |
interface | getPowetoLogQuan |
Generate and return the natural logarithm of the Inverse Cumulative Distribution (Quantile) Function of the (Truncated) Poweto distribution for an input logCDF within the support of the distribution \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).More... | |
interface | getPowetoLogRand |
Generate and return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the (Truncated) Poweto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\). More... | |
interface | setPowetoLogCDF |
Return the natural logarithm of the Cumulative Distribution Function (CDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).More... | |
interface | setPowetoLogPDF |
Return the natural logarithm of the Probability Density Function (PDF) of the (Truncated) Poweto distribution for an input logx within the support of the distribution \(x \in [0 < x_\mathrm{min}, x_\mathrm{max} < +\infty]\).More... | |
interface | setPowetoLogQuan |
Return the natural logarithm of the Inverse Cumulative Distribution (Quantile) Function of the (Truncated) Poweto distribution for an input logCDF within the support of the distribution \((\alpha, x_\mathrm{min}, x_\mathrm{max})\).More... | |
interface | setPowetoLogRand |
Return a scalar (or array of arbitrary rank) of the natural logarithm(s) of random value(s) from the (Truncated) Poweto distribution with parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\). More... | |
Variables | |
character(*, SK), parameter | MODULE_NAME = "@pm_distPoweto" |
This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Power/Pareto distribution (hence the name Poweto).
Specifically, this module contains routines for computing the following quantities of the (Truncated) Power/Pareto distribution:
The (Truncated) Poweto distribution is a generalization of the (Truncated) Pareto and Power distributions.
The PDF of the (Truncated) Poweto distribution over a strictly-positive support \(x \in [x_\mathrm{min}, x_\mathrm{max}]\) is defined with the three (shape, scale, scale) parameters \((\alpha, x_\mathrm{min}, x_\mathrm{max})\) as,
\begin{equation} \large \pi(x | \alpha, x_\mathrm{min}, x_\mathrm{max}) = \eta(\alpha, x_\mathrm{min}, x_\mathrm{max}) ~ x^{\alpha - 1} ~, \end{equation}
where \(\mathbf{-\infty < \alpha < +\infty}\) and \(\mathbf{0 < x_\mathrm{min} \leq x \leq x_\mathrm{max} < +\infty}\) hold, and \(\eta(\alpha, x_\mathrm{min}, x_\mathrm{max})\) is the normalization factor of the PDF.
When \(\alpha = 0\), the (Truncated) Poweto distribution simplifies to the Power-law distribution with exponent \(-1\).
When \(0 < \alpha < +\infty\), the (Truncated) Poweto distribution simplifies to (Truncated) Power distribution.
When \(-\infty < \alpha < 0\), the (Truncated) Poweto distribution simplifies to (Truncated) Pareto distribution.
Final Remarks ⛓
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For details on the naming conventions, see this page.
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character(*, SK), parameter pm_distPoweto::MODULE_NAME = "@pm_distPoweto" |
Definition at line 73 of file pm_distPoweto.F90.