pm_distNegExp Module Reference

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"

Detailed Description

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:

1. the Probability Density Function (PDF)
2. the Cumulative Distribution Function (CDF)
3. the Random Number Generation from the distribution (RNG)
4. the Inverse Cumulative Distribution Function (ICDF) or the Quantile Function

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 \(\mu \leq T < +\infty\).

Note

Note that the mean of the Negative Exponential distribution is the scale parameter: \(\mathrm{mean} = \sigma\)).

See also

pm_distExp
pm_distUnif

Test:

test_pm_distNegExp

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

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

Variable Documentation

MODULE_NAME

character(*, SK), parameter pm_distNegExp::MODULE_NAME = "@pm_distNegExp"

Definition at line 86 of file pm_distNegExp.F90.