#include <STK_Law_Student.h>

Inheritance diagram for STK::Law::Student:

Public Types
typedef IUnivLaw< Real >	Base

Public Member Functions
	Student (int df=1.)
	Default constructor.

virtual	~Student ()
	destructor

int	df () const

void	setDf (int df)

virtual Real	rand () const

virtual Real	pdf (Real const &x) const

virtual Real	lpdf (Real const &x) const

virtual Real	cdf (Real const &t) const

virtual Real	icdf (Real const &p) const

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 (int df)

static Real	pdf (Real const &x, int df)

static Real	lpdf (Real const &x, int df)

static Real	cdf (Real const &t, int df)

static Real	icdf (Real const &p, int df)

Protected Attributes
int	df_
	degree of freedom

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

Student distribution law.

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. Whereas a normal distribution describes a full population, t-distributions describe samples drawn from a full population; accordingly, the t-distribution for each sample size is different, and the larger the sample, the more the distribution resembles a normal distribution.

The t-distribution plays a role in a number of widely used statistical analyses, including the Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. The Student's t-distribution also arises in the Bayesian analysis of data from a normal family

Student's t-distribution has the probability density function given by

$f(t) = \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{t^2}{\nu} \right)^{-\frac{\nu+1}{2}},\!$

where $\nu$ is the number of degrees of freedom.

Definition at line 72 of file STK_Law_Student.h.

Member Typedef Documentation

◆ Base

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

Definition at line 75 of file STK_Law_Student.h.

Constructor & Destructor Documentation

◆ Student()

STK::Law::Student::Student ( int df = 1. )

inline

Default constructor.

Parameters

df	degree of freedom parameter

Definition at line 79 of file STK_Law_Student.h.

79: Base(_T("Student")), df_(df) {}

_T

#define _T(x)

Let x unmodified.

Definition STK_Typedefs.h:71

STK::Law::Student::Base

IUnivLaw< Real > Base

Definition STK_Law_Student.h:75

STK::Law::Student::df_

int df_

degree of freedom

Definition STK_Law_Student.h:145

STK::Law::Student::df

int df() const

Definition STK_Law_Student.h:83

◆ ~Student()

virtual STK::Law::Student::~Student ( )

inlinevirtual

destructor

Definition at line 81 of file STK_Law_Student.h.

81{}

Member Function Documentation

◆ cdf() [1/2]

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

virtual

Returns: the cumulative distribution function

Parameters

t	a positive real value

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

Definition at line 69 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ cdf() [2/2]

Real STK::Law::Student::cdf	(	Real const &	t,
		int	df
	)

static

Returns: the cumulative distribution function

Parameters

t	a positive real value
df	degree of freedom parameter

Definition at line 108 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ df()

int STK::Law::Student::df ( ) const

inline

Returns: the number of degree of freedom

Definition at line 83 of file STK_Law_Student.h.

83{ return df_;}

References df_.

Referenced by setDf().

◆ icdf() [1/2]

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

virtual

Returns: the inverse cumulative distribution function

Parameters

p	a probability number

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

Definition at line 76 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ icdf() [2/2]

Real STK::Law::Student::icdf	(	Real const &	p,
		int	df
	)

static

Returns: the inverse cumulative distribution function

Parameters

p	a probability number
df	degree of freedom parameter

Definition at line 116 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ lpdf() [1/2]

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

virtual

Returns: the value of the log-pdf

Parameters

x	a positive real value

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

Definition at line 62 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ lpdf() [2/2]

Real STK::Law::Student::lpdf	(	Real const &	x,
		int	df
	)

static

Returns: the value of the log-pdf

Parameters

x	a positive real value
df	degree of freedom parameter

Definition at line 100 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ pdf() [1/2]

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

virtual

Returns: the value of the pdf

Parameters

x	a positive real value

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

Definition at line 55 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ pdf() [2/2]

Real STK::Law::Student::pdf	(	Real const &	x,
		int	df
	)

static

Returns: the value of the pdf

Parameters

x	a positive real value
df	degree of freedom parameter

Definition at line 92 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ rand() [1/2]

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

virtual

Returns: a pseudo Student random variate.

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

Definition at line 48 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ rand() [2/2]

Real STK::Law::Student::rand ( int df )

static

Returns: a pseudo Student random variate with the specified parameters.

Parameters

df	degree of freedom parameter

Definition at line 84 of file STK_Law_Student.cpp.

{
  return 0;
}

◆ setDf()

void STK::Law::Student::setDf ( int df )

inline

Parameters

df	degree of freedom parameter

Definition at line 85 of file STK_Law_Student.h.

    {
      if (df<=0) STKDOMAIN_ERROR_1ARG(Student::setShape,df,shape must be > 0);
      df_ = df;
    }

References df(), df_, and STKDOMAIN_ERROR_1ARG.

Member Data Documentation

◆ df_

int STK::Law::Student::df_

protected

degree of freedom

Definition at line 145 of file STK_Law_Student.h.

Referenced by df(), and setDf().

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

◆ Student()

◆ ~Student()

Member Function Documentation

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ df()

◆ icdf() [1/2]

◆ icdf() [2/2]

◆ lpdf() [1/2]

◆ lpdf() [2/2]

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ rand() [1/2]

◆ rand() [2/2]

◆ setDf()

Member Data Documentation

◆ df_