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ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation. |
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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 ⛓
If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.
This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.
| character(*, SK), parameter pm_distPoweto::MODULE_NAME = "@pm_distPoweto" |
Definition at line 73 of file pm_distPoweto.F90.
1.9.3