GammaDistribution Class Reference

marmote: GammaDistribution Class Reference

marmote

marmoteCore is a C++ API dedicated to modeling with Markov chains.

The Gamma distribution with two parameters: shape and scale. More...

#include <marmoteGammaDistribution.h>

Inheritance diagram for GammaDistribution:

Public Member Functions
	GammaDistribution (double shape, double scale)
	Constructor for the Gamma distribution from its shape and scale parameters. The mean is calculated at creation.

double	shape ()

double	rate ()

double	scale ()

double	Mean () const override
	computing the mathematical expectation or mean

double	Rate () const override
	Computation of the "rate", defined as the inverse of the mean.

double	Moment (int order) const override

double	Variance () const override
	Computation of the variance of the random variable: the second moment minus the square of the first moment. Variance is the square of the coefficient of variation. The Distribution class offers a default implementation.

double	Laplace (double s) const override
	Computation of the Laplace transform of the distribution at real point.

double	DLaplace (double s) const override
	Computation of the derivative of the Laplace transform at real points.

double	Cdf (double x) const override
	Computation of the cumulative distribution function at some real point x. This is the probability that the random variable is less or equal to x.

bool	HasMoment (int) const override
	Test for the existence of moments of any order.

GammaDistribution *	Rescale (double factor) const override
	Rescaling a distribution by some real factor. Not all distributions allow this for any real factor. If the operation fails, or if the factor is 1.0, a copy of the distribution should be returned (not by using the Copy() function).

virtual GammaDistribution *	Copy () const override
	Copying a distribution. Implemented by default as Rescale(1.0).

double	Sample () override
	drawing a (pseudo)random value according to the distribution.

void	Write (std::ostream *out, inoutFormat format) const override
	Utility to write the a representation of the distribution to some stream, according to some format.

Public Member Functions inherited from Distribution
	Distribution ()=default
	Standard constructor.

virtual	~Distribution ()=default
	Standard destructor.

std::string	name ()
	Accessor to the type name of the distribution.

virtual double	Ccdf (double x) const
	Computation of the complementary cumulative distributon function (or tail) at some real point x. This is the probability that the random variable is strictly larger than x.

virtual void	IidSample (unsigned long int n, double *s)
	drawing an i.i.d. sample from the distribution. The result is returned in an array (that must have been already allocated) passed as a parameter. The Distribution class offers the default implementation with repeated call to sample().

virtual bool	HasProperty (std::string pro) const
	Property test function. Current properties are:

virtual std::string	toString (inoutFormat format) const
	Utility to convert the distribution into a string.

void	fprint () const
	write on standard output with the standard marmote format

std::string	toString (void) const

Public Member Functions inherited from marmote::Object
	Object (void)

virtual	~Object (void)

const std::string &	className (void) const

void	setClassName (const std::string &)

std::string	toString (void) const

std::string	content (void) const

std::string	info (void) const

Protected Member Functions
std::string	content_impl (void) const override

std::string	info_impl (void) const override

Protected Member Functions inherited from Distribution
std::string	toString_impl (void) const override

Protected Attributes
double	shape_

double	rate_

double	scale_

Protected Attributes inherited from Distribution
std::string	name_

double	mean_ = 0.0

Additional Inherited Members
Static Public Member Functions inherited from Distribution
static double	Distance (distType type, Distribution d1, Distribution d2)
	Computing generally some distance between two distributions.

static double	DistanceL1 (Distribution d1, Distribution d2)
	Computing generally the L1 distance between two distributions.

static double	DistanceL2 (Distribution d1, Distribution d2)
	Computing generally the L2 distance between two distributions.

static double	DistanceLInfinity (Distribution d1, Distribution d2)
	Computing generally the L-infinity distance between two distributions.

static double	DistanceTV (Distribution d1, Distribution d2)
	Computing generally the total variation distance between two distributions.

static double	U_0_1 (void)

static double	Exponential (double Mean)

Static Protected Attributes inherited from Distribution
static const double	VALUE_TOLERANCE = 1.0e-8

static const double	VALUE_SUMPROBAS = 1.0e-10

static const std::string	distance_name [4] = { "L1", "L2", "L-infinity", "TV" }

Detailed Description

The Gamma distribution with two parameters: shape and scale.

Constructor & Destructor Documentation

◆ GammaDistribution()

GammaDistribution::GammaDistribution	(	double	shape,
		double	scale )

Constructor for the Gamma distribution from its shape and scale parameters. The mean is calculated at creation.

Author: Alain Jean-Marie

Parameters

shape	the shape parameter
scale	the rate parameter

Member Function Documentation

◆ Cdf()

double GammaDistribution::Cdf ( double x ) const

overridevirtual

Computation of the cumulative distribution function at some real point x. This is the probability that the random variable is less or equal to x.

Parameters

x	the value at which to compute the cdf

Returns: the value of the cdf

Implements Distribution.

◆ content_impl()

std::string GammaDistribution::content_impl ( void ) const

overrideprotectedvirtual

Reimplemented from marmote::Object.

◆ Copy()

GammaDistribution * GammaDistribution::Copy ( ) const

overridevirtual

Copying a distribution. Implemented by default as Rescale(1.0).

See also: Rescale(double)

Returns: a copy of the distribution

Reimplemented from Distribution.

Reimplemented in ErlangDistribution, and ExponentialDistribution.

◆ DLaplace()

double GammaDistribution::DLaplace ( double s ) const

overridevirtual

Computation of the derivative of the Laplace transform at real points.

Parameters

s	the value at which to compute

Returns: the value of the derivative of the Laplace transform: d LT(s)/ds

Implements Distribution.

◆ HasMoment()

bool GammaDistribution::HasMoment ( int ) const

overridevirtual

Test for the existence of moments of any order.

Parameters

order the order of the moment to be tested

Returns: true if the moment exists, false otherwise

Implements Distribution.

◆ info_impl()

std::string GammaDistribution::info_impl ( void ) const

overrideprotectedvirtual

Reimplemented from marmote::Object.

◆ Laplace()

double GammaDistribution::Laplace ( double s ) const

overridevirtual

Computation of the Laplace transform of the distribution at real point.

Parameters

s	the value at which to compute

Returns: the value of the Laplace transform: LT(s)

Implements Distribution.

◆ Mean()

double GammaDistribution::Mean ( ) const

overridevirtual

computing the mathematical expectation or mean

Returns: the mean

Implements Distribution.

◆ Moment()

double GammaDistribution::Moment ( int order ) const

overridevirtual

These distributions always have a moment.

Implements Distribution.

◆ Rate()

double GammaDistribution::Rate ( ) const

overridevirtual

Computation of the "rate", defined as the inverse of the mean.

Returns: the rate

Implements Distribution.

◆ rate()

double GammaDistribution::rate ( )

inline

◆ Rescale()

GammaDistribution * GammaDistribution::Rescale ( double factor ) const

overridevirtual

Rescaling a distribution by some real factor. Not all distributions allow this for any real factor. If the operation fails, or if the factor is 1.0, a copy of the distribution should be returned (not by using the Copy() function).

See also: Copy()

Parameters

factor the real factor to be used, f

Returns: a new distribution object, the distribution of f.X

Implements Distribution.

◆ Sample()

double GammaDistribution::Sample ( )

overridevirtual

drawing a (pseudo)random value according to the distribution.

Returns: a sample

Implements Distribution.

◆ scale()

double GammaDistribution::scale ( )

inline

◆ shape()

double GammaDistribution::shape ( )

inline

◆ Variance()

double GammaDistribution::Variance ( ) const

overridevirtual

Computation of the variance of the random variable: the second moment minus the square of the first moment. Variance is the square of the coefficient of variation. The Distribution class offers a default implementation.

Returns: the variance

Reimplemented from Distribution.

◆ Write()

void GammaDistribution::Write	(	std::ostream *	out,
		inoutFormat	format ) const

overridevirtual

Utility to write the a representation of the distribution to some stream, according to some format.

Parameters

out	the descriptor of the stream on which to write
format	a code for the output format to be used

Implements Distribution.

Field Documentation

◆ rate_

double GammaDistribution::rate_

protected

rate parameter "beta" of the distribution

◆ scale_

double GammaDistribution::scale_

protected

scale parameter "theta" of the distribution

◆ shape_

double GammaDistribution::shape_

protected

shape parameter "k" of the distribution

The documentation for this class was generated from the following files:

src/marmoteCore/marmoteGammaDistribution.h
src/marmoteCore/marmoteGammaDistribution.cpp

GammaDistribution Class Reference

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ GammaDistribution()

Member Function Documentation

◆ Cdf()

◆ content_impl()

◆ Copy()

◆ DLaplace()

◆ HasMoment()

◆ info_impl()

◆ Laplace()

◆ Mean()

◆ Moment()

◆ Rate()

◆ rate()

◆ Rescale()

◆ Sample()

◆ scale()

◆ shape()

◆ Variance()

◆ Write()

Field Documentation

◆ rate_

◆ scale_

◆ shape_