Generate a random variate from a Student's t-distribution. More...

#include <StudentT.h>

Inheritance diagram for honey::StudentT_< Real >:

Collaboration diagram for honey::StudentT_< Real >:

Classes
struct	PooledStats

struct	Stats

Public Types
typedef Random::DistStats	DistStats

typedef Vec< 2, Real >	Vec2

Public Member Functions
	StudentT_ (optional< RandomGen & > gen, Real n)

	StudentT_ (Real n)

virtual Real	next () const
	Get next randomly distributed variate. Requires a random generator (see ctor or setGen()) More...

virtual Real	pdf (Real x) const
	Probability Density Function. More...

virtual Real	cdf (Real x) const
	Cumulative Distribution Function. More...

virtual Real	cdfComp (Real x) const
	Complement of the CDF. More...

virtual Real	cdfInv (Real P) const
	Inverse of the CDF. More...

virtual Real	mean () const
	Calc mean. More...

virtual Real	variance () const
	Calc variance. More...

Public Member Functions inherited from honey::RandomDist< Real >
	RandomDist (optional< RandomGen & > gen=optnull)
	Construct with a random generator to use for next() More...

virtual	~RandomDist ()

Real	stdDev () const
	Calc standard deviation. More...

void	setGen (RandomGen &gen)
	Set random generator to use for next() More...

RandomGen &	getGen () const
	Get random generator. More...

Static Public Member Functions
template<class Range >
static bool	test (const Range &samples, optional< Stats & > stats=optnull, Real mu=0, Real alpha=0.05, int tail=0)
	One-sample t-test: Test the null hypothesis that the samples are from a normally distributed population with mean `mu` and unknown standard deviation. More...

template<class Range , class Range2 >
static std::enable_if< mt::isRange< Range2 >::value, bool >::type	test (const Range &samples1, const Range2 &samples2, optional< PooledStats & > stats=optnull, Real mu=0, Real alpha=0.05, int tail=0)
	Two-sample t-test: Test the null hypothesis that the difference between two sample distributions is a normally distributed population with mean `mu` and unknown standard deviation. More...

Public Attributes
Real	n

Additional Inherited Members
Protected Types inherited from honey::RandomDist< Real >
typedef Numeral< Real >::Real_	Real_

typedef Real_::DoubleType	Double_

typedef Double_::Real	Double

typedef Alge_< Real >	Alge

typedef Alge_< Double >	Alge_d

typedef Uniform_< Double >	Uniform

Protected Member Functions inherited from honey::RandomDist< Real >
Real	cdfInvFind (Real P, Real min, Real max, bool discrete=false) const
	Generic binary search algorithm to find Cdf. More...

Detailed Description

template<class Real>
class honey::StudentT_< Real >

Generate a random variate from a Student's t-distribution.

The t-dist can be used to account for uncertainty when estimating a quantity (such as the mean) from a small sample of a normally distributed population. The estimation of the quantity produces additive errors that the t-dist can account for.

The shape of the curve is wider than a normal curve, allowing samples to fall further from the mean. As the degrees of freedom increase, the t-distribution approaches the normal distribution.

Probability density function:

$\displaystyle p(x,n) = \frac{\Gamma \paren*{ \frac{n+1}{2}} } {\sqrt{n\pi} \; \Gamma \paren*{ \frac{n}{2} }} \paren*{1 + \frac{x^2}{n}}^{\!\! -\frac{n+1}{2}}$

Parameters

n	Number of degrees of freedom. Range > 0

Return values

x	Random variate. Range [-inf,inf]

Member Typedef Documentation

template<class Real >

typedef Random::DistStats honey::StudentT_< Real >::DistStats

template<class Real >

typedef Vec<2,Real> honey::StudentT_< Real >::Vec2

Constructor & Destructor Documentation

template<class Real >

honey::StudentT_< Real >::StudentT_	(	optional< RandomGen & >	gen,
		Real	n
	)

inline

template<class Real >

honey::StudentT_< Real >::StudentT_ ( Real n )

inline

Member Function Documentation

template<class Real >

Real honey::StudentT_< Real >::cdf ( Real x ) const

virtual

Cumulative Distribution Function.

The integral of the PDF from -inf to x.

Parameters

x	value, range depends on distribution.

Return values

P	a probability in range [0,1] that a random variate will be <= x.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::StudentT_< Real >::cdfComp ( Real x ) const

virtual

Complement of the CDF.

The integral of the PDF from x to inf.

Parameters

x	value, range depends on distribution.

Return values

Q	a probability in range [0,1] that a random variate will be > x.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::StudentT_< Real >::cdfInv ( Real P ) const

virtual

Inverse of the CDF.

Parameters

P	cumulative probability

Return values

x	A value that has probability P of being >= a random variate X. Also, x satisfies: cdf(x) = P.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

virtual Real honey::StudentT_< Real >::mean ( ) const

inlinevirtual

Calc mean.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::StudentT_< Real >::next ( ) const

virtual

Get next randomly distributed variate. Requires a random generator (see ctor or setGen())

Reimplemented from honey::RandomDist< Real >.

template<class Real >

Real honey::StudentT_< Real >::pdf ( Real x ) const

virtual

Probability Density Function.

The PDF integrates to 1 over the entire range of possible values of x.

Parameters

x	value, range depends on distribution.

Return values

p	a relative likelihood in range [0,inf] that a random variate X will equal x.

Reimplemented from honey::RandomDist< Real >.

template<class Real >

template<class Range >

static bool honey::StudentT_< Real >::test	(	const Range &	samples,
		optional< Stats & >	stats = `optnull`,
		Real	mu = `0`,
		Real	alpha = `0.05`,
		int	tail = `0`
	)

inlinestatic

One-sample t-test: Test the null hypothesis that the samples are from a normally distributed population with mean mu and unknown standard deviation.

Parameters

samples	Sample set to test
stats	Statistics about the test may be optionally retrieved
mu	The mean to test
alpha	The test is performed at the (100*alpha)% significance level, default is 5%
tail	0 = two-tailed test (true if mean is not mu) 1 = upper tail test (true if mean is > mu) -1 = lower tail test (true if mean is < mu)

Returns: Returns true if the null hypothesis is rejected and thus the mean is not mu. If the result is true at 5% significance then there is at most a 1 in 20 chance that the null hypothesis was incorrectly rejected.

template<class Real >

template<class Range , class Range2 >

static std::enable_if<mt::isRange<Range2>::value, bool>::type honey::StudentT_< Real >::test	(	const Range &	samples1,
		const Range2 &	samples2,
		optional< PooledStats & >	stats = `optnull`,
		Real	mu = `0`,
		Real	alpha = `0.05`,
		int	tail = `0`
	)

inlinestatic

Two-sample t-test: Test the null hypothesis that the difference between two sample distributions is a normally distributed population with mean mu and unknown standard deviation.

This test assumes that both sample distributions have the same variance.

Parameters

samples1	First sample set to test
samples2	Second sample set to test
stats	Statistics about the test may be optionally retrieved
mu	The mean to test
alpha	The test is performed at the (100*alpha)% significance level, default is 5%
tail	0 = two-tailed test (true if mean (1-2) is not mu) 1 = upper tail test (true if mean (1-2) > mu) -1 = lower tail test (true if mean (1-2) < mu)

Returns: Returns true if the null hypothesis is rejected and thus the mean (1-2) is not mu. If the result is true at 5% significance then there is at most a 1 in 20 chance that the null hypothesis was incorrectly rejected.

template<class Real >

virtual Real honey::StudentT_< Real >::variance ( ) const

inlinevirtual

Calc variance.

Reimplemented from honey::RandomDist< Real >.

Member Data Documentation

template<class Real >

Real honey::StudentT_< Real >::n

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

src/common/Honey/Math/Random/Dist/StudentT.h
src/common/Honey/Math/Random/Dist/StudentT.cpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

template<class Real> class honey::StudentT_< Real >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Real>
class honey::StudentT_< Real >