class for the Uniform law distribution. More...

#include <STK_Law_UniformDiscrete.h>

Inheritance diagram for STK::Law::UniformDiscrete:

Public Types
typedef IUnivLaw< int >	Base

Public Member Functions
	UniformDiscrete (int a, int b)
	constructor.

	UniformDiscrete (UniformDiscrete const &law)
	copy constructor.

virtual	~UniformDiscrete ()
	destructor.

int const &	a () const

int const &	b () const

Real const &	n () const

void	setA (int a)

void	setB (int b)

virtual int	rand () const
	Generate a pseudo Uniform random variate.

virtual Real	pdf (int const &x) const
	Give the value of the pdf at x.

virtual Real	lpdf (int const &x) const
	Give the value of the log-pdf at x.

virtual Real	cdf (Real const &t) const
	The cumulative distribution function is.

virtual int	icdf (Real const &p) const
	The inverse cumulative distribution function is.

Public Member Functions inherited from STK::Law::IUnivLaw< int >
virtual	~IUnivLaw ()
	Virtual destructor.

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

Static Public Member Functions
static int	rand (int a, int b)
	Generate a pseudo Uniform random variate.

static Real	pdf (Real const &x, int a, int b)
	Give the value of the pdf at x.

static Real	lpdf (Real const &p, int a, int b)
	Give the value of the log-pdf at x.

static Real	cdf (Real const &t, int a, int b)
	Give the value of the cdf at t.

static int	icdf (Real const &p, int a, int b)
	Give the value of the quantile at p.

Protected Attributes
int	a_
	The lower bound.

int	b_
	The upper bound.

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

Private Attributes
Real	n_

Additional Inherited Members
Protected Member Functions inherited from STK::Law::IUnivLaw< int >
	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.

Detailed Description

class for the Uniform law distribution.

In probability theory and statistics, the discrete uniform distribution is a probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

The probability density function of the discrete uniform distribution is:

$f(x; a, b) = \frac{1}{b-a+1} 1_{ a \leq x \leq b}, \quad a,b,x\in\mathbb{N}.$

Definition at line 58 of file STK_Law_UniformDiscrete.h.

Member Typedef Documentation

◆ Base

typedef IUnivLaw<int> STK::Law::UniformDiscrete::Base

Definition at line 61 of file STK_Law_UniformDiscrete.h.

Constructor & Destructor Documentation

◆ UniformDiscrete() [1/2]

STK::Law::UniformDiscrete::UniformDiscrete	(	int	a,
		int	b
	)

inline

constructor.

Parameters

a,b	the lower and upper bounds

Definition at line 65 of file STK_Law_UniformDiscrete.h.

                                         : Base(_T("UniformDiscrete")), a_(a), b_(b), n_(b_ - a_ + 1)
    {
      if (n_ < 0.)
      { STKINVALIDARGUMENT_ERROR_2ARG(UniformDiscrete::UniformDiscrete, a_, b_,invalid parameters);}
    }

References a_, b_, n_, STKINVALIDARGUMENT_ERROR_2ARG, and UniformDiscrete().

Referenced by UniformDiscrete().

◆ UniformDiscrete() [2/2]

STK::Law::UniformDiscrete::UniformDiscrete ( UniformDiscrete const & law )

inline

copy constructor.

Parameters

law	the law to copy

Definition at line 73 of file STK_Law_UniformDiscrete.h.

74 : Base(law), a_(law.a_), b_(law.b_), n_(law.n_)

75 {}

◆ ~UniformDiscrete()

virtual STK::Law::UniformDiscrete::~UniformDiscrete ( )

inlinevirtual

destructor.

Definition at line 77 of file STK_Law_UniformDiscrete.h.

77{}

Member Function Documentation

◆ a()

int const & STK::Law::UniformDiscrete::a ( ) const

inline

Returns: the lower bound

Definition at line 79 of file STK_Law_UniformDiscrete.h.

79{ return a_;}

References a_.

Referenced by cdf(), icdf(), lpdf(), pdf(), rand(), and setA().

◆ b()

int const & STK::Law::UniformDiscrete::b ( ) const

inline

Returns: the upper bound

Definition at line 81 of file STK_Law_UniformDiscrete.h.

81{ return b_;}

References b_.

Referenced by cdf(), icdf(), lpdf(), pdf(), rand(), and setB().

◆ cdf() [1/2]

Real STK::Law::UniformDiscrete::cdf ( Real const & t ) const

virtual

The cumulative distribution function is.

$F(t; a,b)= \frac{t - a}{b-a}$

Parameters

t	a real value

Implements STK::Law::IUnivLaw< int >.

Definition at line 75 of file STK_Law_UniformDiscrete.cpp.

{
  if (!Arithmetic<Real>::isFinite(t) ) return t;
  if (t <= a_) return 0.;
  if (t >= b_) return 1.;
  return (b_ - (int)t)/n_;
}

References a_, b_, and n_.

◆ cdf() [2/2]

Real STK::Law::UniformDiscrete::cdf	(	Real const &	t,
		int	a,
		int	b
	)

static

Give the value of the cdf at t.

Parameters

t	a real value
a,b	the lower and upper bounds

Definition at line 130 of file STK_Law_UniformDiscrete.cpp.

131{ return (b - t)/(b-a+1);}

References a(), and b().

◆ icdf() [1/2]

int STK::Law::UniformDiscrete::icdf ( Real const & p ) const

virtual

The inverse cumulative distribution function is.

$F^{-1}(p; \lambda) = p (b-a) + a.$

Parameters

p	a probability

Implements STK::Law::IUnivLaw< int >.

Definition at line 89 of file STK_Law_UniformDiscrete.cpp.

{
  // check parameter
  if ((p > 1.) || (p < 0.))
    STKDOMAIN_ERROR_1ARG(Exponential::icdf,p,invalid argument);
 
  if (!Arithmetic<Real>::isFinite(p) ) return p;
  if (p == 1.) return b_;
  if (p == 0.) return a_;
  return(int)((1.-p) * a_ + p * b_);
}

References a_, b_, STK::Law::Exponential::icdf(), and STKDOMAIN_ERROR_1ARG.

◆ icdf() [2/2]

int STK::Law::UniformDiscrete::icdf	(	Real const &	p,
		int	a,
		int	b
	)

static

Give the value of the quantile at p.

Parameters

p	a probability
a,b	the lower and upper bounds

Definition at line 134 of file STK_Law_UniformDiscrete.cpp.

135{ return (int)((1.-p) * a + p * b);}

References a(), and b().

◆ lpdf() [1/2]

Real STK::Law::UniformDiscrete::lpdf ( int const & x ) const

virtual

Give the value of the log-pdf at x.

Parameters

x	a real value

Reimplemented from STK::Law::IUnivLaw< int >.

Definition at line 63 of file STK_Law_UniformDiscrete.cpp.

{
  if (!Arithmetic<Real>::isFinite(x) ) return x;
  if ((x < a_)||(x > b_)) return -Arithmetic<Real>::infinity();
  return -std::log(n_);
}

References a_, b_, and n_.

◆ lpdf() [2/2]

Real STK::Law::UniformDiscrete::lpdf	(	Real const &	p,
		int	a,
		int	b
	)

static

Give the value of the log-pdf at x.

Parameters

p	a probablility
a,b	the lower and upper bounds

Definition at line 123 of file STK_Law_UniformDiscrete.cpp.

{
  if (!Arithmetic<Real>::isFinite(x) ) return x;
  if ((x < a)||(x > b)) return -Arithmetic<Real>::infinity();
  return -std::log(b-a+1);
}

References a(), and b().

◆ n()

Real const & STK::Law::UniformDiscrete::n ( ) const

inline

Returns: the value b-a+1

Definition at line 83 of file STK_Law_UniformDiscrete.h.

83{ return n_;}

References n_.

◆ pdf() [1/2]

Real STK::Law::UniformDiscrete::pdf ( int const & x ) const

virtual

Give the value of the pdf at x.

Parameters

x	a real value

Implements STK::Law::IUnivLaw< int >.

Definition at line 54 of file STK_Law_UniformDiscrete.cpp.

{
  if (!Arithmetic<Real>::isFinite(x) ) return x;
  if ((x < a_)||(x > b_)) return 0.;
  return 1./n_;
}

References a_, b_, and n_.

◆ pdf() [2/2]

Real STK::Law::UniformDiscrete::pdf	(	Real const &	x,
		int	a,
		int	b
	)

static

Give the value of the pdf at x.

Parameters

x	a real value
a,b	the lower and upper bounds

Definition at line 112 of file STK_Law_UniformDiscrete.cpp.

{
  if (!Arithmetic<Real>::isFinite(x) ) return x;
  if ((x < a)||(x > b)) return 0.;
  return 1./Real(b-a+1);
}

References a(), and b().

◆ rand() [1/2]

int STK::Law::UniformDiscrete::rand ( ) const

virtual

Generate a pseudo Uniform random variate.

Implements STK::Law::IUnivLaw< int >.

Definition at line 49 of file STK_Law_UniformDiscrete.cpp.

50{ return a_ + int(generator.rand(double(n_)));}

int

References a_, and n_.

Referenced by STK::CvHandler::partition(), STK::PartitionHandler::partition(), STK::HDMatrixGaussianModel< IdRow_, IdCol_, Array_ >::randomInit(), STK::DiagGaussianBase< Derived >::randomMean(), and STK::HDGaussianBase< Derived >::randomMean().

◆ rand() [2/2]

int STK::Law::UniformDiscrete::rand	(	int	a,
		int	b
	)

static

Generate a pseudo Uniform random variate.

Parameters

a,b	the lower and upper bounds

Definition at line 105 of file STK_Law_UniformDiscrete.cpp.

106{ return a + int(generator.rand(double(b - a +1)));}

References a(), and b().

◆ setA()

void STK::Law::UniformDiscrete::setA ( int a )

inline

Parameters

a	set the lower bound

Definition at line 85 of file STK_Law_UniformDiscrete.h.

85{ a_ =a; n_ = b_-a_+1;}

References a(), a_, b_, and n_.

◆ setB()

void STK::Law::UniformDiscrete::setB ( int b )

inline

Parameters

b	set the upper bound

Definition at line 87 of file STK_Law_UniformDiscrete.h.

87{ b_ =b; n_ = b_ - a_ + 1;}

References a_, b(), b_, and n_.

Member Data Documentation

◆ a_

int STK::Law::UniformDiscrete::a_

protected

The lower bound.

Definition at line 141 of file STK_Law_UniformDiscrete.h.

Referenced by a(), cdf(), icdf(), lpdf(), pdf(), rand(), setA(), setB(), and UniformDiscrete().

◆ b_

int STK::Law::UniformDiscrete::b_

protected

The upper bound.

Definition at line 143 of file STK_Law_UniformDiscrete.h.

Referenced by b(), cdf(), icdf(), lpdf(), pdf(), setA(), setB(), and UniformDiscrete().

◆ n_

Real STK::Law::UniformDiscrete::n_

private

Definition at line 146 of file STK_Law_UniformDiscrete.h.

Referenced by cdf(), lpdf(), n(), pdf(), rand(), setA(), setB(), and UniformDiscrete().

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

Constructor & Destructor Documentation

◆ UniformDiscrete() [1/2]

◆ UniformDiscrete() [2/2]

◆ ~UniformDiscrete()

Member Function Documentation

◆ a()

◆ b()

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ icdf() [1/2]

◆ icdf() [2/2]

◆ lpdf() [1/2]

◆ lpdf() [2/2]

◆ n()

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ rand() [1/2]

◆ rand() [2/2]

◆ setA()

◆ setB()

Member Data Documentation

◆ a_

◆ b_

◆ n_