Extends the class ContinuousDistribution for the Fisher F distribution with \(n_1\) and \(n_2\) degrees of freedom, where \(n_1\) and \(n_2\) are positive integers. More...

Inheritance diagram for FisherFDist:

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Collaboration diagram for FisherFDist:

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Public Member Functions
	FisherFDist (int n1, int n2)
	Constructs a Fisher \(F\) distribution with `n1` and `n2` degrees of freedom.

double	density (double x)

double	cdf (double x)
	Returns the distribution function \(F(x)\). More...

double	barF (double x)
	Returns \(\bar{F}(x) = 1 - F(x)\). More...

double	inverseF (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...

double	getMean ()
	Returns the mean of the distribution function.

double	getVariance ()
	Returns the variance of the distribution function.

double	getStandardDeviation ()
	Returns the standard deviation of the distribution function.

int	getN ()
	Returns the parameter `n1` of this object.

int	getM ()
	Returns the parameter `n2` of this object.

int	getN1 ()
	Returns the parameter `n1` of this object.

int	getN2 ()
	Returns the parameter `n2` of this object.

void	setParams (int n1, int n2)
	Sets the parameters `n1` and `n2` of this object.

double []	getParams ()
	Return a table containing the parameters of the current distribution. More...

String	toString ()
	Returns a `String` containing information about the current distribution.

Public Member Functions inherited from ContinuousDistribution
abstract double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\). More...

double	barF (double x)
	Returns the complementary distribution function. More...

double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...

double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...

double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\). More...

double	getMean ()
	Returns the mean. More...

double	getVariance ()
	Returns the variance. More...

double	getStandardDeviation ()
	Returns the standard deviation. More...

double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXinf (double xa)
	Sets the value \(x_a=\) `xa`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXsup (double xb)
	Sets the value \(x_b=\) `xb`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

Static Public Member Functions
static double	density (int n1, int n2, double x)
	Computes the density function ( FisherF ) for a Fisher \(F\) distribution with `n1` and `n2` degrees of freedom, evaluated at \(x\).

static double	cdf (int n1, int n2, int d, double x)
	Computes the distribution function of the Fisher \(F\) distribution with parameters `n1` and `n2`, evaluated at \(x\), with roughly \(d\) decimal digits of precision.

static double	cdf (int n1, int n2, double x)
	Computes the distribution function of the Fisher \(F\) distribution with parameters `n1` and `n2`, evaluated at \(x\).

static double	barF (int n1, int n2, int d, double x)
	Computes the complementary distribution function of the Fisher \(F\) distribution with parameters `n1` and `n2`, evaluated at \(x\), with roughly \(d\) decimal digits of precision.

static double	barF (int n1, int n2, double x)
	Computes the complementary distribution function of the Fisher \(F\) distribution with parameters `n1` and `n2`, evaluated at \(x\).

static double	inverseF (int n1, int n2, int d, double u)
	Computes the inverse of the Fisher \(F\) distribution with parameters `n1` and `n2`, evaluated at \(u\), with roughly \(d\) decimal digits of precision.

static double	inverseF (int n1, int n2, double u)
	Computes the inverse of the Fisher \(F\) distribution with parameters `n1` and `n2`, evaluated at \(u\).

static double	getMean (int n1, int n2)
	Computes and returns the mean \(E[X] = n_2 / (n_2 - 2)\) of the Fisher \(F\) distribution with parameters `n1` and `n2` \(=n_2\). More...

static double	getVariance (int n1, int n2)
	Computes and returns the variance \[ \mbox{Var}[X] = \frac{2n_2^2 (n_2 + n_1 - 2)}{n_1 (n_2 - 2)^2 (n_2 - 4)} \] of the Fisher \(F\) distribution with parameters `n1` \(=n_1\) and `n2` \(=n_2\). More...

static double	getStandardDeviation (int n1, int n2)
	Computes and returns the standard deviation of the Fisher \(F\) distribution with parameters `n1` and `n2`. More...

Protected Attributes
int	n1

int	n2

double	C1

Protected Attributes inherited from ContinuousDistribution
double	supportA = Double.NEGATIVE_INFINITY

double	supportB = Double.POSITIVE_INFINITY

Additional Inherited Members
Public Attributes inherited from ContinuousDistribution
int	decPrec = 15

Static Protected Attributes inherited from ContinuousDistribution
static final double	XBIG = 100.0

static final double	XBIGM = 1000.0

static final double []	EPSARRAY

Detailed Description

Extends the class ContinuousDistribution for the Fisher F distribution with \(n_1\) and \(n_2\) degrees of freedom, where \(n_1\) and \(n_2\) are positive integers.

Its density is

\[ f(x) = \frac{\Gamma(\frac{n_1 + n_2}{2})n_1^{\frac{n_1}{2}}n_2^{\frac{n_2}{2}}}{\Gamma(\frac{n_1}{2})\Gamma(\frac{n_2}{2})} \frac{x^{\frac{n_1 - 2}{2}}}{(n_2 + n_1x)^{\frac{n_1 + n_2}{2}}}, \qquad\mbox{for } x > 0 \tag{FisherF} \]

where \(\Gamma(x)\) is the gamma function defined in ( Gamma ).

Member Function Documentation

◆ barF()

double barF ( double x )

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Implements Distribution.

◆ cdf()

double cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements Distribution.

◆ getMean()

static double getMean	(	int	n1,
		int	n2
	)

static

Computes and returns the mean \(E[X] = n_2 / (n_2 - 2)\) of the Fisher \(F\) distribution with parameters n1 and n2 \(=n_2\).

Returns: the mean of the Fisher \(F\) distribution

◆ getParams()

double [] getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [n1, n2].

Implements Distribution.

◆ getStandardDeviation()

static double getStandardDeviation	(	int	n1,
		int	n2
	)

static

Computes and returns the standard deviation of the Fisher \(F\) distribution with parameters n1 and n2.

Returns: the standard deviation of the Fisher \(F\) distribution

◆ getVariance()

static double getVariance	(	int	n1,
		int	n2
	)

static

Computes and returns the variance

\[ \mbox{Var}[X] = \frac{2n_2^2 (n_2 + n_1 - 2)}{n_1 (n_2 - 2)^2 (n_2 - 4)} \]

of the Fisher \(F\) distribution with parameters n1 \(=n_1\) and n2 \(=n_2\).

Returns: the variance of the Fisher \(F\) distribution \(\mbox{Var}[X] = (2n2^2 (n2 + n1 - 2)) / (n1 (n2 - 2)^2 (n2 - 4))\)

◆ inverseF()

double inverseF ( double u )

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters

u	value in the interval \((0,1)\) for which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Implements Distribution.

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

FisherFDist.java

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ barF()

◆ cdf()

◆ getMean()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()