Interface base class for all the univariate distributions. More...

#include <STK_Law_IUnivLaw.h>

Inheritance diagram for STK::Law::IUnivLaw< Type >:

Public Member Functions
virtual	~IUnivLaw ()
	Virtual destructor.

virtual Type	rand () const =0

virtual Real	pdf (Type const &x) const =0
	compute the probability distribution function (density) in the continuous case and the probability mass function in the discrete case.

virtual Type	icdf (Real const &p) const =0
	inverse cumulative distribution function The quantile is defined as the smallest value x such that F(x) >= p , where F is the cumulative distribution function.

virtual Real	lpdf (Type const &x) const
	compute the log probability distribution function Give the value of the log-pdf at the point x.

virtual Real	cdf (Real const &t) const =0
	compute the lower tail cumulative distribution function Give the probability that a random variate is less or equal to t.

virtual Real	lcdf (Real const &t) const
	compute the lower tail log-cumulative distribution function Give the log-probability that a random variate is less or equal to t.

virtual Real	cdfc (Real const &t) const
	calculate the complement of cumulative distribution function, called in statistics the survival function.

virtual Real	lcdfc (Real const &t) const
	calculate the log-complement of cumulative distribution function Give the log-probability that a random variate is greater than t.

Public Member Functions inherited from STK::Law::ILawBase
String const &	name () const

Protected Member Functions
	IUnivLaw (String const &name)
	Constructor.

	IUnivLaw (IUnivLaw const &law)
	copy Constructor.

Protected Member Functions inherited from STK::Law::ILawBase
	ILawBase (String const &name)
	Constructor.

	~ILawBase ()
	destructor.

Additional Inherited Members
Protected Attributes inherited from STK::Law::ILawBase
String	name_
	Name of the Law.

Detailed Description

template<class Type>
class STK::Law::IUnivLaw< Type >

Interface base class for all the univariate distributions.

A general probability law (discrete or real) possess a probability distribution function (pdf), a cumulative distribution function (cdt) and an inverse cumulative distribution function (icdf). It can be simulated (random number generation).

Interface base class for the univariate distributions. Every derived class have to furnish :

a random generator method
Type rand() const

STK::Law::IUnivLaw::rand
virtual Type rand() const =0

STK::MultidimRegression
The MultidimRegression class allows to regress a multidimensional output variable among a multivariat...
Definition STK_MultidimRegression.h:52
a probability distribution function (pdf)
Real pdf(Type const& x) const

STK::Law::IUnivLaw::pdf
virtual Real pdf(Type const &x) const =0
compute the probability distribution function (density) in the continuous case and the probability ma...

STK::Real
double Real
STK fundamental type of Real values.
Definition STK_Typedefs.h:118
a log-probability distribution function (log-pdf)
Real lpdf(Type const& x) const

STK::Law::IUnivLaw::lpdf
virtual Real lpdf(Type const &x) const
compute the log probability distribution function Give the value of the log-pdf at the point x.
Definition STK_Law_IUnivLaw.h:108
a quantile method (inverse cdf)
Type icdf(Real const& p) const

STK::Law::IUnivLaw::icdf
virtual Type icdf(Real const &p) const =0
inverse cumulative distribution function The quantile is defined as the smallest value x such that F...

.

The derived objects should also furnish the same static functions. Instantiation of a derived object is interesting when one want to simulate independent identical distributed random variates: at creation, the object initializes all parameter-dependent variables.

Definition at line 71 of file STK_Law_IUnivLaw.h.

Constructor & Destructor Documentation

◆ IUnivLaw() [1/2]

template<class Type >

STK::Law::IUnivLaw< Type >::IUnivLaw ( String const & name )

inlineprotected

Constructor.

Parameters

name	the name of the law

Definition at line 77 of file STK_Law_IUnivLaw.h.

77: ILawBase(name) {}

STK::Law::ILawBase::ILawBase

ILawBase(String const &name)

Constructor.

Definition STK_Law_ILawBase.h:59

STK::Law::ILawBase::name

String const & name() const

Definition STK_Law_ILawBase.h:65

◆ IUnivLaw() [2/2]

template<class Type >

STK::Law::IUnivLaw< Type >::IUnivLaw ( IUnivLaw< Type > const & law )

inlineprotected

copy Constructor.

Parameters

law	the law to copy

Definition at line 81 of file STK_Law_IUnivLaw.h.

81: ILawBase(law.name_) {}

◆ ~IUnivLaw()

template<class Type >

virtual STK::Law::IUnivLaw< Type >::~IUnivLaw ( )

inlinevirtual

Virtual destructor.

Definition at line 85 of file STK_Law_IUnivLaw.h.

85{}

Member Function Documentation

◆ cdf()

template<class Type >

virtual Real STK::Law::IUnivLaw< Type >::cdf ( Real const & t ) const

pure virtual

compute the lower tail cumulative distribution function Give the probability that a random variate is less or equal to t.

Parameters

t	a real number

Returns: the value of the cdf

Implemented in STK::Law::Bernoulli, STK::Law::Beta, STK::Law::Binomial, STK::Law::Categorical, STK::Law::Cauchy, STK::Law::ChiSquared, STK::Law::Exponential, STK::Law::FisherSnedecor, STK::Law::Gamma, STK::Law::Geometric, STK::Law::HyperGeometric, STK::Law::Logistic, STK::Law::LogNormal, STK::Law::NegativeBinomial, STK::Law::Normal, STK::Law::Poisson, STK::Law::Student, STK::Law::Uniform, STK::Law::UniformDiscrete, and STK::Law::Weibull.

Referenced by STK::Law::IUnivLaw< Type >::cdfc(), and STK::Law::IUnivLaw< Type >::lcdf().

◆ cdfc()

template<class Type >

virtual Real STK::Law::IUnivLaw< Type >::cdfc ( Real const & t ) const

inlinevirtual

calculate the complement of cumulative distribution function, called in statistics the survival function.

Give the probability that a random variate is greater than t.

Parameters

t	a real number

Returns: the value of the cdf

Definition at line 126 of file STK_Law_IUnivLaw.h.

126{ return(1. - cdf(t));}

STK::Law::IUnivLaw::cdf

virtual Real cdf(Real const &t) const =0

compute the lower tail cumulative distribution function Give the probability that a random variate is...

References STK::Law::IUnivLaw< Type >::cdf().

Referenced by STK::Law::IUnivLaw< Type >::lcdfc(), and main().

◆ icdf()

template<class Type >

virtual Type STK::Law::IUnivLaw< Type >::icdf ( Real const & p ) const

pure virtual

inverse cumulative distribution function The quantile is defined as the smallest value x such that F(x) >= p , where F is the cumulative distribution function.

Parameters

p	a probability

Implemented in STK::Law::Beta, STK::Law::Binomial, STK::Law::Cauchy, STK::Law::ChiSquared, STK::Law::Exponential, STK::Law::FisherSnedecor, STK::Law::Gamma, STK::Law::Geometric, STK::Law::HyperGeometric, STK::Law::Logistic, STK::Law::LogNormal, STK::Law::NegativeBinomial, STK::Law::Normal, STK::Law::Poisson, STK::Law::Student, STK::Law::Uniform, STK::Law::UniformDiscrete, STK::Law::Weibull, STK::Law::Bernoulli, and STK::Law::Categorical.

◆ lcdf()

template<class Type >

virtual Real STK::Law::IUnivLaw< Type >::lcdf ( Real const & t ) const

inlinevirtual

compute the lower tail log-cumulative distribution function Give the log-probability that a random variate is less or equal to t.

Parameters

t	a real number

Returns: the value of the cdf

Definition at line 120 of file STK_Law_IUnivLaw.h.

120{ return(std::log(cdf(t)));}

References STK::Law::IUnivLaw< Type >::cdf().

Referenced by main().

◆ lcdfc()

template<class Type >

virtual Real STK::Law::IUnivLaw< Type >::lcdfc ( Real const & t ) const

inlinevirtual

calculate the log-complement of cumulative distribution function Give the log-probability that a random variate is greater than t.

Parameters

t	a real number

Returns: the value of the cdf

Definition at line 132 of file STK_Law_IUnivLaw.h.

132{ return(std::log(cdfc(t)));}

STK::Law::IUnivLaw::cdfc

virtual Real cdfc(Real const &t) const

calculate the complement of cumulative distribution function, called in statistics the survival funct...

Definition STK_Law_IUnivLaw.h:126

References STK::Law::IUnivLaw< Type >::cdfc().

Referenced by main().

◆ lpdf()

template<class Type >

virtual Real STK::Law::IUnivLaw< Type >::lpdf ( Type const & x ) const

inlinevirtual

compute the log probability distribution function Give the value of the log-pdf at the point x.

Parameters

x	the value to compute the lpdf.

Returns: the value of the log-pdf

Reimplemented in STK::Law::Bernoulli, STK::Law::Categorical, STK::Law::Poisson, STK::Law::UniformDiscrete, STK::Law::Binomial, STK::Law::Geometric, STK::Law::HyperGeometric, STK::Law::NegativeBinomial, STK::Law::Beta, STK::Law::Cauchy, STK::Law::ChiSquared, STK::Law::Exponential, STK::Law::FisherSnedecor, STK::Law::Gamma, STK::Law::Logistic, STK::Law::LogNormal, STK::Law::Normal, STK::Law::Student, STK::Law::Uniform, and STK::Law::Weibull.

Definition at line 108 of file STK_Law_IUnivLaw.h.

108{ return(std::log(pdf(x)));}

References STK::Law::IUnivLaw< Type >::pdf().

◆ pdf()

template<class Type >

virtual Real STK::Law::IUnivLaw< Type >::pdf ( Type const & x ) const

pure virtual

compute the probability distribution function (density) in the continuous case and the probability mass function in the discrete case.

Parameters

x	the value to compute the pdf.

Returns: the value of the pdf

Implemented in STK::Law::Bernoulli, STK::Law::Categorical, STK::Law::Poisson, STK::Law::UniformDiscrete, STK::Law::Binomial, STK::Law::Geometric, STK::Law::HyperGeometric, STK::Law::NegativeBinomial, STK::Law::Beta, STK::Law::Cauchy, STK::Law::ChiSquared, STK::Law::Exponential, STK::Law::FisherSnedecor, STK::Law::Gamma, STK::Law::Logistic, STK::Law::LogNormal, STK::Law::Normal, STK::Law::Student, STK::Law::Uniform, and STK::Law::Weibull.

Referenced by STK::Law::IUnivLaw< Type >::lpdf().

◆ rand()

template<class Type >

virtual Type STK::Law::IUnivLaw< Type >::rand ( ) const

pure virtual

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

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ IUnivLaw() [1/2]

◆ IUnivLaw() [2/2]

◆ ~IUnivLaw()

Member Function Documentation

◆ cdf()

◆ cdfc()

◆ icdf()

◆ lcdf()

◆ lcdfc()

◆ lpdf()

◆ pdf()

◆ rand()