Generate a random integer variate from a poisson distribution. More...

#include <Poisson.h>

Inheritance diagram for honey::Poisson_< Real >:

Collaboration diagram for honey::Poisson_< Real >:

Public Member Functions
	Poisson_ (RandomGen &gen, Real mu)

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...

Static Public Member Functions
static Real	eventMean (Int x, Real P)
	Calculate mean given all other values. More...

Public Attributes
Real	mu

Friends
template<class >
class	Poisson_

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::Poisson_< Real >

Generate a random integer variate from a poisson distribution.

A poisson distribution can be used to count the number of events in a period of time if these events are independent from each other and occur at an average rate.

The result x is an integer number of events.

Example:

Number of particles emitted by radioactive decay per minute.
Number of times a web server is accessed per minute.

Probability density function:

$\displaystyle p(x,\mu) = \frac{\mu^x e^{-\mu}}{x!}$

Parameters

mu	$\mu$ Mean, expected number of occurances per interval. Range > 0

Return values

x	Number of events. Result range: [0,inf]

Constructor & Destructor Documentation

template<class Real >

honey::Poisson_< Real >::Poisson_	(	RandomGen &	gen,
		Real	mu
	)

inline

Member Function Documentation

template<class Real >

Real honey::Poisson_< 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::Poisson_< 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::Poisson_< 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 >

Real honey::Poisson_< Real >::eventMean	(	Int	x,
		Real	P
	)

static

Calculate mean given all other values.

Finds the mean mu such that x or fewer number of events will occur in the interval, with a probability of P

template<class Real >

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

inlinevirtual

Calc mean.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

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

inlinevirtual

Calc variance.

Reimplemented from honey::RandomDist< Real >.

Friends And Related Function Documentation

template<class Real >

template<class >

friend class Poisson_

friend

Member Data Documentation

template<class Real >

Real honey::Poisson_< Real >::mu

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

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

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Additional Inherited Members

Detailed Description

template<class Real> class honey::Poisson_< Real >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<class Real>
class honey::Poisson_< Real >