#include <STK_Law_Logistic.h>

Inheritance diagram for STK::Law::Logistic:

Public Types
typedef IUnivLaw< Real >	Base

Public Member Functions
	Logistic (Real const &mu=0., Real const &scale=1.)
	Constructor.

virtual	~Logistic ()
	Destructor.

Real const &	mu () const

Real const &	scale () const

void	setMu (Real const &mu)

void	setScale (Real const &scale)

Real	rand () const
	Generate a pseudo Logistic random variate.

virtual Real	pdf (Real const &x) const

virtual Real	lpdf (Real const &x) const

virtual Real	cdf (Real const &t) const
	Compute the cumulative distribution function at t of the standard logistic distribution.

virtual Real	icdf (Real const &p) const
	Compute the inverse cumulative distribution function at p of the standard logistic distribution.

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 &mu, Real const &scale)
	Generate a pseudo Logistic random variate with location `mu` and scale `scale` parameters.

static Real	pdf (Real const &x, Real const &mu, Real const &scale)

static Real	lpdf (Real const &x, Real const &mu, Real const &scale)

static Real	cdf (Real const &t, Real const &mu, Real const &scale)

static Real	icdf (Real const &p, Real const &mu, Real const &scale)

Protected Attributes
Real	mu_
	The mu parameter.

Real	scale_
	The scale parameter.

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

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

Logistic distribution law.

In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the logistic distribution in shape but has heavier tails (higher kurtosis).

The Logistic distribution with location = m and scale = s>0 has distribution function

$F(x) = 1 / (1 + exp(-(x-m)/s))$

and density

$f(x) = \frac{1}{s} \frac{exp\left(\frac{x-m}{s}\right)} {\left(1 + exp\left(\frac{x-m}{s}\right)\right)^2}.$

It is a long-tailed distribution with mean m and variance $\frac{π^2s^2}{3}$ .

Definition at line 67 of file STK_Law_Logistic.h.

Member Typedef Documentation

◆ Base

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

Definition at line 70 of file STK_Law_Logistic.h.

Constructor & Destructor Documentation

◆ Logistic()

STK::Law::Logistic::Logistic	(	Real const &	mu = `0.`,
		Real const &	scale = `1.`
	)

inline

Constructor.

Parameters

mu	mean of the Logistic distribution
scale	scale of the Logistic distribution

Definition at line 75 of file STK_Law_Logistic.h.

76 : Base(_T("Logistic")), mu_(mu), scale_(scale) {}

_T

#define _T(x)

Let x unmodified.

Definition STK_Typedefs.h:71

STK::Law::Logistic::scale_

Real scale_

The scale parameter.

Definition STK_Law_Logistic.h:175

STK::Law::Logistic::Base

IUnivLaw< Real > Base

Definition STK_Law_Logistic.h:70

STK::Law::Logistic::mu_

Real mu_

The mu parameter.

Definition STK_Law_Logistic.h:173

STK::Law::Logistic::scale

Real const & scale() const

Definition STK_Law_Logistic.h:82

STK::Law::Logistic::mu

Real const & mu() const

Definition STK_Law_Logistic.h:80

◆ ~Logistic()

virtual STK::Law::Logistic::~Logistic ( )

inlinevirtual

Destructor.

Definition at line 78 of file STK_Law_Logistic.h.

78{}

Member Function Documentation

◆ cdf() [1/2]

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

virtual

Compute the cumulative distribution function at t of the standard logistic distribution.

The cumulative distribution function of the logistic distribution is also a scaled version of the Hyperbolic function.

$F(t; \mu, s) = \frac{1}{1+e^{-\frac{t-\mu}{s}}} = \frac{1}{2} + \frac{1}{2} \;\operatorname{tanh}\!\left(\frac{t-\mu}{2s}\right).$

Parameters

t	a real value

Returns: the cumulative distribution function value at t

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

Definition at line 83 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ cdf() [2/2]

Real STK::Law::Logistic::cdf	(	Real const &	t,
		Real const &	mu,
		Real const &	scale
	)

static

Returns: the cumulative distribution function value at t.

Parameters

t	a real value
mu,scale	location and scale of the Logistic distribution

Definition at line 142 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ icdf() [1/2]

Real STK::Law::Logistic::icdf ( Real const & p ) const

virtual

Compute the inverse cumulative distribution function at p of the standard logistic distribution.

The inverse cumulative distribution function (quantile function) of the logistic distribution is a generalization of the logit function. It is defined as follows:

$Q(p;\mu,s) = \mu + s\,\ln\left(\frac{p}{1-p}\right).$

Parameters

p	a probability number.

Returns: the inverse cumulative distribution function value at p.

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

Definition at line 100 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ icdf() [2/2]

Real STK::Law::Logistic::icdf	(	Real const &	p,
		Real const &	mu,
		Real const &	scale
	)

static

Returns: the inverse cumulative distribution function value at p.

Parameters

p	a probability number.
mu,scale	location and scale of the Logistic distribution

Definition at line 153 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ lpdf() [1/2]

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

virtual

Returns: 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_Logistic.cpp.

{
  return 0;
}

◆ lpdf() [2/2]

Real STK::Law::Logistic::lpdf	(	Real const &	x,
		Real const &	mu,
		Real const &	scale
	)

static

Returns: Give the value of the log-pdf at x.

Parameters

x	a real value
mu,scale	location and scale of the Logistic distribution

Definition at line 132 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ mu()

Real const & STK::Law::Logistic::mu ( ) const

inline

Returns: mu

Definition at line 80 of file STK_Law_Logistic.h.

80{ return mu_;}

References mu_.

Referenced by setMu().

◆ pdf() [1/2]

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

virtual

Parameters

x	a real value

Returns: the value of the logistic pdf at x

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

Definition at line 59 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ pdf() [2/2]

Real STK::Law::Logistic::pdf	(	Real const &	x,
		Real const &	mu,
		Real const &	scale
	)

static

Parameters

x	a real value
mu,scale	location and scale of the Logistic distribution

Returns: the value of the logistic pdf at x

Definition at line 123 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ rand() [1/2]

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

virtual

Generate a pseudo Logistic random variate.

Generate a pseudo Logistic random variate with location parameter mu_ and scale scale_.

Returns: a pseudo logistic random variate

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

Definition at line 52 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ rand() [2/2]

Real STK::Law::Logistic::rand	(	Real const &	mu,
		Real const &	scale
	)

static

Generate a pseudo Logistic random variate with location mu and scale scale parameters.

scale scale parameters.

Parameters

mu,scale location and scale of the Logistic distribution

Returns: a pseudo logistic random variate, centered in mu and with scale scale

Definition at line 114 of file STK_Law_Logistic.cpp.

{
  return 0;
}

◆ scale()

Real const & STK::Law::Logistic::scale ( ) const

inline

Returns: mu

Definition at line 82 of file STK_Law_Logistic.h.

82{ return scale_;}

References scale_.

Referenced by setScale().

◆ setMu()

void STK::Law::Logistic::setMu ( Real const & mu )

inline

Parameters

mu	the value to set to mu

Definition at line 84 of file STK_Law_Logistic.h.

84{ mu_ = mu;}

References mu(), and mu_.

◆ setScale()

void STK::Law::Logistic::setScale ( Real const & scale )

inline

Parameters

scale the value to set to scale

Definition at line 86 of file STK_Law_Logistic.h.

    {
      if (scale<=0) STKDOMAIN_ERROR_1ARG(Logistic::setScale,scale,scale must be > 0);
       scale_ = scale;
    }

References scale(), scale_, setScale(), and STKDOMAIN_ERROR_1ARG.

Referenced by setScale().

Member Data Documentation

◆ mu_

Real STK::Law::Logistic::mu_

protected

The mu parameter.

Definition at line 173 of file STK_Law_Logistic.h.

Referenced by mu(), and setMu().

◆ scale_

Real STK::Law::Logistic::scale_

protected

The scale parameter.

Definition at line 175 of file STK_Law_Logistic.h.

Referenced by scale(), and setScale().

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

Constructor & Destructor Documentation

◆ Logistic()

◆ ~Logistic()

Member Function Documentation

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ icdf() [1/2]

◆ icdf() [2/2]

◆ lpdf() [1/2]

◆ lpdf() [2/2]

◆ mu()

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ rand() [1/2]

◆ rand() [2/2]

◆ scale()

◆ setMu()

◆ setScale()

Member Data Documentation

◆ mu_

◆ scale_