class for the Uniform law distribution. More...

#include <STK_Law_Uniform.h>

Inheritance diagram for STK::Law::Uniform:

Public Types
typedef IUnivLaw< Real >	Base

Public Member Functions
	Uniform (Real const &a=0., Real const &b=1.)
	constructor.

	Uniform (Uniform const &law)
	copy constructor.

virtual	~Uniform ()
	destructor.

Real const &	a () const

Real const &	b () const

Real const &	range () const

void	setA (Real const &a)

void	setB (Real const &b)

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

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

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

Public Member Functions inherited from STK::Law::IUnivLaw< Real >
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 Real	rand (Real const &a, Real const &b)
	Generate a pseudo Uniform random variate.

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

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

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

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

Protected Attributes
Real	a_
	The lower bound.

Real	b_
	The upper bound.

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

Private Attributes
Real	range_

Additional Inherited Members
Protected Member Functions inherited from STK::Law::IUnivLaw< Real >
	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 continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values.

The probability density function of the continuous uniform distribution is:

$f(x; a, b) = \frac{1}{b-a} 1_{ a \leq x \leq b}.$

Definition at line 59 of file STK_Law_Uniform.h.

Member Typedef Documentation

◆ Base

typedef IUnivLaw<Real> STK::Law::Uniform::Base

Definition at line 62 of file STK_Law_Uniform.h.

Constructor & Destructor Documentation

◆ Uniform() [1/2]

STK::Law::Uniform::Uniform	(	Real const &	a = `0.`,
		Real const &	b = `1.`
	)

inline

constructor.

Parameters

a,b	the lower and upper bounds

Definition at line 66 of file STK_Law_Uniform.h.

                 : Base(_T("Uniform")), a_(a), b_(b), range_(b_ - a_)
    {
      if (range_ <= 0.)
        STKINVALIDARGUMENT_ERROR_2ARG(Uniform::Uniform, a_, b_,invalid parameters);
    }

References a_, b_, range_, STKINVALIDARGUMENT_ERROR_2ARG, and Uniform().

Referenced by Uniform().

◆ Uniform() [2/2]

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

inline

copy constructor.

Parameters

law	the law to copy

Definition at line 75 of file STK_Law_Uniform.h.

75 : Base(law), a_(law.a_), b_(law.b_), range_(law.range_)

76 {};

◆ ~Uniform()

virtual STK::Law::Uniform::~Uniform ( )

inlinevirtual

destructor.

Definition at line 78 of file STK_Law_Uniform.h.

78{}

Member Function Documentation

◆ a()

Real const & STK::Law::Uniform::a ( ) const

inline

Returns: the lower bound

Definition at line 80 of file STK_Law_Uniform.h.

80{ return a_;}

References a_.

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

◆ b()

Real const & STK::Law::Uniform::b ( ) const

inline

Returns: the upper bound

Definition at line 82 of file STK_Law_Uniform.h.

82{ return b_;}

References b_.

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

◆ cdf() [1/2]

Real STK::Law::Uniform::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< Real >.

Definition at line 78 of file STK_Law_Uniform.cpp.

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

References a_, b_, and range_.

◆ cdf() [2/2]

Real STK::Law::Uniform::cdf	(	Real const &	t,
		Real const &	a,
		Real const &	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 134 of file STK_Law_Uniform.cpp.

135{ return (b - t)/(b-a);}

References a(), and b().

◆ icdf() [1/2]

Real STK::Law::Uniform::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< Real >.

Definition at line 92 of file STK_Law_Uniform.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 a_ + p * range_;
}

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

◆ icdf() [2/2]

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

static

Give the value of the quantile at p.

Parameters

p	a probability
a,b	the lower and upper bounds

Definition at line 138 of file STK_Law_Uniform.cpp.

139{ return std::max(a,std::min((1.-p) * a + p * b, b));}

References a(), and b().

◆ lpdf() [1/2]

Real STK::Law::Uniform::lpdf	(	Real const &	p,
		Real const &	a,
		Real const &	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 127 of file STK_Law_Uniform.cpp.

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

References a(), and b().

◆ lpdf() [2/2]

Real STK::Law::Uniform::lpdf ( Real const & x ) const

virtual

Give the value of the log-pdf at x.

Parameters

x	a real value

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

Definition at line 66 of file STK_Law_Uniform.cpp.

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

References a_, b_, and range_.

◆ pdf() [1/2]

Real STK::Law::Uniform::pdf ( Real const & x ) const

virtual

Give the value of the pdf at x.

Parameters

x	a real value

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

Definition at line 57 of file STK_Law_Uniform.cpp.

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

References a_, b_, and range_.

◆ pdf() [2/2]

Real STK::Law::Uniform::pdf	(	Real const &	x,
		Real const &	a,
		Real const &	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 117 of file STK_Law_Uniform.cpp.

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

References a(), and b().

◆ rand() [1/2]

Real STK::Law::Uniform::rand ( ) const

virtual

Generate a pseudo Uniform random variate.

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

Definition at line 49 of file STK_Law_Uniform.cpp.

{
  return ((range_ <= 1.) || (a_ <=1.)) ? a_ + range_ * generator.randUnif()
                                       : a_ * (1. + generator.randUnif()*range_/a_) ;
}

References a_, and range_.

◆ rand() [2/2]

Real STK::Law::Uniform::rand	(	Real const &	a,
		Real const &	b
	)

static

Generate a pseudo Uniform random variate.

Parameters

a,b	the lower and upper bounds

Definition at line 108 of file STK_Law_Uniform.cpp.

{
  return( (b-a <= 1.) ? a + (b-a) * generator.randUnif()
                      : a + generator.rand(b-a));
}

References a(), and b().

◆ range()

Real const & STK::Law::Uniform::range ( ) const

inline

Returns: the value b-a

Definition at line 84 of file STK_Law_Uniform.h.

84{ return range_;}

References range_.

◆ setA()

void STK::Law::Uniform::setA ( Real const & a )

inline

Parameters

a	set the lower bound

Definition at line 86 of file STK_Law_Uniform.h.

86{ a_ =a;}

References a(), and a_.

◆ setB()

void STK::Law::Uniform::setB ( Real const & b )

inline

Parameters

b	set the upper bound

Definition at line 88 of file STK_Law_Uniform.h.

88{ b_ =b;}

References b(), and b_.

Member Data Documentation

◆ a_

Real STK::Law::Uniform::a_

protected

The lower bound.

Definition at line 151 of file STK_Law_Uniform.h.

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

◆ b_

Real STK::Law::Uniform::b_

protected

The upper bound.

Definition at line 153 of file STK_Law_Uniform.h.

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

◆ range_

Real STK::Law::Uniform::range_

private

Definition at line 156 of file STK_Law_Uniform.h.

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

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

◆ Uniform() [1/2]

◆ Uniform() [2/2]

◆ ~Uniform()

Member Function Documentation

◆ a()

◆ b()

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ icdf() [1/2]

◆ icdf() [2/2]

◆ lpdf() [1/2]

◆ lpdf() [2/2]

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ rand() [1/2]

◆ rand() [2/2]

◆ range()

◆ setA()

◆ setB()

Member Data Documentation

◆ a_

◆ b_

◆ range_