Generate a normally (Gaussian) distributed random variate. More...

#include <Gaussian.h>

Inheritance diagram for honey::Gaussian_< Real >:

Collaboration diagram for honey::Gaussian_< Real >:

Public Member Functions
	Gaussian_ (optional< RandomGen & > gen, Real mu=0, Real sigma=1)

	Gaussian_ (Real mu=0, Real sigma=1)

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	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 ()

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

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...

Static Public Member Functions
static Real	erf (Real x)
	Gauss Error Function, related to Cdf. Input: [-inf, inf] -> Output: [-1, 1]. More...

static Real	erfComp (Real x)
	Complement of Error Function. More...

static Real	erfInv (Real y)
	Inverse of Error Function, related to CdfInv. Input: [-1, 1] -> Output: [-inf, inf]. More...

static Real	erfCompInv (Real y)
	Inverse of complement Error Function. More...

Public Attributes
Real	mu

Real	sigma

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::Gaussian_< Real >

Generate a normally (Gaussian) distributed random variate.

The gaussian distribution is a core component for most other distributions.

Example: Toss a coin 1000 times and count number of heads

Probability density function:

$\displaystyle p(x,\mu,\sigma) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

Default values provide the standard normal distribution around 0

Parameters

mu	$\mu$ Mean
sigma	$\sigma$ Standard deviation. Range > 0

Return values

x	Random variate. Range [-inf, inf]

Constructor & Destructor Documentation

template<class Real >

honey::Gaussian_< Real >::Gaussian_	(	optional< RandomGen & >	gen,
		Real	mu = `0`,
		Real	sigma = `1`
	)

inline

template<class Real >

honey::Gaussian_< Real >::Gaussian_	(	Real	mu = `0`,
		Real	sigma = `1`
	)

inline

Member Function Documentation

template<class Real >

Real honey::Gaussian_< 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::Gaussian_< 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 >

static Real honey::Gaussian_< Real >::erf ( Real x )

inlinestatic

Gauss Error Function, related to Cdf. Input: [-inf, inf] -> Output: [-1, 1].

template<class Real >

static Real honey::Gaussian_< Real >::erfComp ( Real x )

inlinestatic

Complement of Error Function.

template<class Real >

static Real honey::Gaussian_< Real >::erfCompInv ( Real y )

inlinestatic

Inverse of complement Error Function.

template<class Real >

static Real honey::Gaussian_< Real >::erfInv ( Real y )

inlinestatic

Inverse of Error Function, related to CdfInv. Input: [-1, 1] -> Output: [-inf, inf].

template<class Real >

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

inlinevirtual

Calc mean.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::Gaussian_< 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::Gaussian_< 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::Gaussian_< Real >::variance ( ) const

inlinevirtual

Calc variance.

Reimplemented from honey::RandomDist< Real >.

Member Data Documentation

template<class Real >

Real honey::Gaussian_< Real >::mu

template<class Real >

Real honey::Gaussian_< Real >::sigma

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

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

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

template<class Real> class honey::Gaussian_< Real >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Real>
class honey::Gaussian_< Real >