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 n₁ and n₂ degrees of freedom, where n₁ and n₂ are positive integers. Its density is

f (x) = Γ((n₁ + n₂)/2)n₁^n₁/2n₂^n₂/2/[Γ(n₁/2)Γ(n₂/2)]x^(n₁-2)/2/(n₂ + n₁x)^{(n₁+n₂)/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

FisherFDist(int n1, int n2)
Constructs a Fisher F distribution with n1 and n2 degrees of freedom.

Method Summary

double	barF(double x) Returns the complementary distribution function.
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	barF(int n1, int n2, int d, double x) Deprecated.
double	cdf(double x) Returns the distribution function F(x).
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	cdf(int n1, int n2, int d, double x) Deprecated.
double	density(double x) Returns f (x), the density evaluated at x.
static double	density(int n1, int n2, double x) Computes the density function for a Fisher F distribution with n1 and n2 degrees of freedom, evaluated at x.
int	getM() Deprecated.
double	getMean() Returns the mean.
static double	getMean(int n1, int n2) Computes and returns the mean E[X] = n2/(n2 - 2) of the Fisher F distribution with parameters n1 and n2 = n2.
int	getN() Deprecated.
int	getN1() Returns the parameter n1 of this object.
int	getN2() Returns the parameter n2 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 n1, int n2) Computes and returns the standard deviation of the Fisher F distribution with parameters n1 and n2.
double	getVariance() Returns the variance.
static double	getVariance(int n1, int n2) Computes and returns the variance of the Fisher F distribution with parameters n1 = n1 and n2 = n2.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
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	inverseF(int n1, int n2, int d, double u) Deprecated.
void	setParams(int n1, int n2) Sets the parameters n1 and n2 of this object.
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 n1,
                   int n2)

Constructs a Fisher F distribution with n1 and n2 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 n1,
                             int n2,
                             double x)

Computes the density function for a Fisher F distribution with n1 and n2 degrees of freedom, evaluated at x.

cdf

@Deprecated
public static double cdf(int n1,
                                    int n2,
                                    int d,
                                    double x)

Deprecated.

cdf

public 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.

barF

@Deprecated
public static double barF(int n1,
                                     int n2,
                                     int d,
                                     double x)

Deprecated.

barF

public 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.

inverseF

@Deprecated
public static double inverseF(int n1,
                                         int n2,
                                         int d,
                                         double u)

Deprecated.

inverseF

public 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.

getMean

public static double getMean(int n1,
                             int n2)

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

Returns:

the mean of the Fisher F distribution

getVariance

public static double getVariance(int n1,
                                 int n2)

Computes and returns the variance of the Fisher F distribution with parameters n1 = n₁ and n2 = n₂.

Returns:

the variance of the Fisher F distribution Var[X] = (2n2²(n2 + n1 - 2))/(n1(n2 - 2)²(n2 - 4))

getStandardDeviation

public static double getStandardDeviation(int n1,
                                          int n2)

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

getN

@Deprecated
public int getN()

Deprecated.

Returns the parameter n1 of this object.

getM

@Deprecated
public int getM()

Deprecated.

getN1

public int getN1()

Returns the parameter n1 of this object.

getN2

public int getN2()

Returns the parameter n2 of this object.

setParams

public void setParams(int n1,
                      int n2)

Sets the parameters n1 and n2 of this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution. This table is put in regular order: [n1, n2].

toString

public String toString()

Overrides:

toString in class Object