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 Negative Exponential distribution. More...
Data Types | |
type | distNegExp_type |
This is the derived type for signifying distributions that are of type Negative Exponential as defined in the description of pm_distNegExp. More... | |
interface | getNegExpCDF |
Generate and return the Cumulative Distribution Function (CDF) of the Negative Exponential distribution for an input x within the support of the distribution \((-\infty, \mu]\). More... | |
interface | getNegExpLogPDF |
Generate and return the natural logarithm of the Probability Density Function (PDF) of the Negative Exponential distribution for an input x within the support of the distribution \((-\infty, \mu]\). More... | |
interface | getNegExpRand |
Return a scalar (or array of arbitrary rank of) random value(s) from the Negative Exponential distribution, optionally with the specified input location and scale parameters mu, sigma .More... | |
interface | setNegExpCDF |
Return the Cumulative Distribution Function (CDF) of the Negative Exponential distribution for an input x within the support of the distribution \((-\infty, \mu]\). More... | |
interface | setNegExpLogPDF |
Return the natural logarithm of the Probability Density Function (PDF) of the Negative Exponential distribution for an input x within the support of the distribution \((-\infty, \mu]\). More... | |
interface | setNegExpRand |
Return a scalar (or array of arbitrary rank of) random value(s) from the Negative Exponential distribution, optionally with the specified input location and scale parameters mu, sigma .More... | |
Variables | |
character(*, SK), parameter | MODULE_NAME = "@pm_distNegExp" |
This module contains classes and procedures for computing various statistical quantities related to the Negative Exponential distribution.
Specifically, this module contains routines for computing the following quantities of the Negative Exponential distribution:
The PDF of the Negative Exponential distribution with the two location and scale parameters \((\mu, \sigma)\) is defined as,
\begin{equation} \large F(x | \mu, \sigma) = \begin{cases} \frac{1}{\sigma} \exp(\frac{x - \mu}{\sigma}) &,~ -\infty < x \leq \mu \\ 0 &,~ x > \mu \end{cases} \end{equation}
where \(-\infty < \mu < +\infty\) is the location parameter and \(0 < \sigma < +\infty\) is the scale parameter of the distribution.
The corresponding CDF with the two location and scale parameters \((\mu, \sigma)\) is defined as,
\begin{equation} \large \ms{CDF}(x | \mu, \sigma) = \begin{cases} \exp(\frac{x - \mu}{\sigma}) &,~ -\infty < x \leq \mu \\ 0 &,~ x > \mu \end{cases} \end{equation}
where \(-\infty < \mu < +\infty\) is the location parameter and \(0 < \sigma < +\infty\) is the scale parameter of the distribution.
Random Number Generation
Assuming \(U \in (0, 1]\) is a uniformly-distributed random variate,
\begin{equation} \large T = \sigma\log(U) + \mu ~, \end{equation}
is a random variate from the Negative Exponential distribution with the location parameter \(-\infty < \mu < +\infty\) and the scale parameter \(0 < \sigma < +\infty\) such that \(\mu \leq T < +\infty\).
Final Remarks ⛓
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character(*, SK), parameter pm_distNegExp::MODULE_NAME = "@pm_distNegExp" |
Definition at line 86 of file pm_distNegExp.F90.