Generate a random variate from a gamma distribution $\mathrm{Gamma}$ . More...

#include <Gamma.h>

Inheritance diagram for honey::Gamma_< Real >:

Collaboration diagram for honey::Gamma_< Real >:

Public Member Functions
	Gamma_ (optional< RandomGen & > gen, Real a, Real b)

	Gamma_ (Real a, Real b)

virtual Real	next () const
	Get next randomly distributed variate. Requires a random generator (see ctor or setGen()) More...

virtual Real	pdf (Real x) const
	Probability Density Function. More...

virtual Real	cdf (Real x) const
	Cumulative Distribution Function. More...

virtual Real	cdfComp (Real x) const
	Complement of the CDF. More...

virtual Real	cdfInv (Real P) const
	Inverse of the CDF. More...

virtual Real	mean () const
	Calc mean. More...

virtual Real	variance () const
	Calc variance. More...

Public Member Functions inherited from honey::RandomDist< Real >
	RandomDist (optional< RandomGen & > gen=optnull)
	Construct with a random generator to use for next() More...

virtual	~RandomDist ()

Real	stdDev () const
	Calc standard deviation. More...

void	setGen (RandomGen &gen)
	Set random generator to use for next() More...

RandomGen &	getGen () const
	Get random generator. More...

Public Attributes
Real	a

Real	b

Additional Inherited Members
Protected Types inherited from honey::RandomDist< Real >
typedef Numeral< Real >::Real_	Real_

typedef Real_::DoubleType	Double_

typedef Double_::Real	Double

typedef Alge_< Real >	Alge

typedef Alge_< Double >	Alge_d

typedef Uniform_< Double >	Uniform

Protected Member Functions inherited from honey::RandomDist< Real >
Real	cdfInvFind (Real P, Real min, Real max, bool discrete=false) const
	Generic binary search algorithm to find Cdf. More...

Detailed Description

template<class Real>
class honey::Gamma_< Real >

Generate a random variate from a gamma distribution $\mathrm{Gamma}$ .

The gamma distribution is a core component for most other distributions. It is a distribution of the amount of time required for a number of events to occur – the opposite of a poisson distribution.

Example: Waiting time until death

Probability density function:

$\displaystyle p(x,\alpha,\beta) = \frac{1}{\Gamma(\alpha) \beta^\alpha} x^{\alpha-1} e^{-x / \beta}$ where $\Gamma$ is the gamma function.

Parameters

a	Shape parameter alpha $\alpha$ (aka. k). Range > 0
b	Scale parameter beta $\beta$ (aka. theta $\theta$ ). Range > 0

Return values

x	Random variate. Range [0,inf]

Constructor & Destructor Documentation

template<class Real >

honey::Gamma_< Real >::Gamma_	(	optional< RandomGen & >	gen,
		Real	a,
		Real	b
	)

inline

template<class Real >

honey::Gamma_< Real >::Gamma_	(	Real	a,
		Real	b
	)

inline

Member Function Documentation

template<class Real >

Real honey::Gamma_< Real >::cdf ( Real x ) const

virtual

Cumulative Distribution Function.

The integral of the PDF from -inf to x.

Parameters

x	value, range depends on distribution.

Return values

P	a probability in range [0,1] that a random variate will be <= x.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::Gamma_< Real >::cdfComp ( Real x ) const

virtual

Complement of the CDF.

The integral of the PDF from x to inf.

Parameters

x	value, range depends on distribution.

Return values

Q	a probability in range [0,1] that a random variate will be > x.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::Gamma_< Real >::cdfInv ( Real P ) const

virtual

Inverse of the CDF.

Parameters

P	cumulative probability

Return values

x	A value that has probability P of being >= a random variate X. Also, x satisfies: cdf(x) = P.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

virtual Real honey::Gamma_< Real >::mean ( ) const

inlinevirtual

Calc mean.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::Gamma_< Real >::next ( ) const

virtual

Get next randomly distributed variate. Requires a random generator (see ctor or setGen())

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::Gamma_< Real >::pdf ( Real x ) const

virtual

Probability Density Function.

The PDF integrates to 1 over the entire range of possible values of x.

Parameters

x	value, range depends on distribution.

Return values

p	a relative likelihood in range [0,inf] that a random variate X will equal x.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

virtual Real honey::Gamma_< Real >::variance ( ) const

inlinevirtual

Calc variance.

Reimplemented from honey::RandomDist< Real >.

Member Data Documentation

template<class Real >

Real honey::Gamma_< Real >::a

template<class Real >

Real honey::Gamma_< Real >::b

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

src/common/Honey/Math/Random/Dist/Gamma.h
src/common/Honey/Math/Random/Dist/Gamma.cpp

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

template<class Real> class honey::Gamma_< Real >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Real>
class honey::Gamma_< Real >