umontreal.iro.lecuyer.probdist

Class FisherFDist

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.FisherFDist

All Implemented Interfaces:

Distribution

public class FisherFDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Fisher F distribution with n and m degrees of freedom, where n and m are positive integers. Its density is

f (x) = Γ((n + m)/2)n^n/2m^m/2/[Γ(n/2)Γ(m/2)]x^(n-2)/2/(m + nx)^(n+m)/2, for x > 0.

where Γ(x) is the gamma function defined in GammaDist.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

Constructors

Constructor and Description
FisherFDist(int n, int m) Constructs a Fisher F distribution with n and m degrees of freedom.

Method Summary

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
static double	barF(int n, int m, int d, double x) Computes the complementary distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(int n, int m, int d, double x) Computes the distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
double	density(double x) Returns f (x), the density evaluated at x.
static double	density(int n, int m, double x) Computes the density function for a Fisher F distribution with n and m degrees of freedom.
int	getM() Returns the parameter m of this object.
double	getMean() Returns the mean.
static double	getMean(int n, int m) Computes and returns the mean E[X] = m/(m - 2) of the Fisher F distribution with parameters n and m.
int	getN() Returns the parameter n of this object.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the standard deviation.
static double	getStandardDeviation(int n, int m) Computes and returns the standard deviation of the Fisher F distribution with parameters n and m.
double	getVariance() Returns the variance.
static double	getVariance(int n, int m) Computes and returns the variance of the Fisher F distribution with parameters n and m.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(int n, int m, int d, double u) Computes the inverse of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
void	setParams(int n, int m) Sets the parameters n and m of this object.
java.lang.String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

FisherFDist

public FisherFDist(int n,
                   int m)

Constructs a Fisher F distribution with n and m degrees of freedom.

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density evaluated at x.

Specified by:

density in class ContinuousDistribution

Parameters:

x - value at which the density is evaluated

Returns:

density function evaluated at x

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Parameters:

x - value at which the distribution function is evaluated

Returns:

distribution function evaluated at x

barF

public double barF(double x)

Description copied from class: ContinuousDistribution

Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Overrides:

barF in class ContinuousDistribution

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

complementary distribution function evaluated at x

inverseF

public double inverseF(double u)

Description copied from class: ContinuousDistribution

Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

getMean

public double getMean()

Description copied from class: ContinuousDistribution

Returns the mean.

Specified by:

getMean in interface Distribution

Overrides:

getMean in class ContinuousDistribution

Returns:

the mean

getVariance

public double getVariance()

Description copied from class: ContinuousDistribution

Returns the variance.

Specified by:

getVariance in interface Distribution

Overrides:

getVariance in class ContinuousDistribution

Returns:

the variance

getStandardDeviation

public double getStandardDeviation()

Description copied from class: ContinuousDistribution

Returns the standard deviation.

Specified by:

getStandardDeviation in interface Distribution

Overrides:

getStandardDeviation in class ContinuousDistribution

Returns:

the standard deviation

density

public static double density(int n,
                             int m,
                             double x)

Computes the density function for a Fisher F distribution with n and m degrees of freedom.

cdf

public static double cdf(int n,
                         int m,
                         int d,
                         double x)

Computes the distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.

barF

public static double barF(int n,
                          int m,
                          int d,
                          double x)

Computes the complementary distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.

inverseF

public static double inverseF(int n,
                              int m,
                              int d,
                              double u)

Computes the inverse of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.

getMean

public static double getMean(int n,
                             int m)

Computes and returns the mean E[X] = m/(m - 2) of the Fisher F distribution with parameters n and m.

Returns:

the mean of the Fisher F distribution

getVariance

public static double getVariance(int n,
                                 int m)

Computes and returns the variance of the Fisher F distribution with parameters n and m.

Returns:

the variance of the Fisher F distribution Var[X] = (2m²(m + n - 2))/(n(m - 2)²(m - 4))

getStandardDeviation

public static double getStandardDeviation(int n,
                                          int m)

Computes and returns the standard deviation of the Fisher F distribution with parameters n and m.

Returns:

the standard deviation of the Fisher F distribution

getN

public int getN()

Returns the parameter n of this object.

getM

public int getM()

Returns the parameter m of this object.

setParams

public void setParams(int n,
                      int m)

Sets the parameters n and m of this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution. This table is put in regular order: [n, m].

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object